, Microwave Office Element Catalog, tech. report, National Instruments, 2019.

V. Acary, O. Bonnefon, and B. Brogliato, Nonsmooth Modeling and Simulation for Switched Circuits, Lecture Notes in Electrical Engineering, vol.69, 2011.
URL : https://hal.archives-ouvertes.fr/inria-00522358

V. Acary, M. Brémond, and O. Huber, On solving contact problems with Coulomb friction: formulations and numerical comparisons, Transactions of the European Network for Nonsmooth Dynamics, pp.375-457, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01878539

V. Acary and B. Brogliato, Lecture Notes in Applied and Computational Mechanics, vol.35, 2008.

V. Acary and B. Brogliato, Implicit Euler numerical scheme and chattering-free implementation of sliding mode systems, Systems and Control Letters, vol.59, pp.284-293, 2010.
URL : https://hal.archives-ouvertes.fr/inria-00423576

V. Acary, B. Brogliato, and D. Goeleven, Higher order Moreau's sweeping process: Mathematical formulation and numerical simulation, Mathematical Programming A, vol.113, pp.133-217, 2008.

V. Acary, H. Jong, and B. Brogliato, Numerical simulation of piecewise-linear models of gene regulatory networks using complementarity systems, Physica D: Nonlinear Phenomena, vol.269, pp.103-119, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00924044

L. Adam and J. Outrata, On optimal control of a sweeping process coupled with an ordinary differential equation, Discrete and Continuous Dynamical Systems -Series B, vol.19, pp.2709-2738, 2014.

K. Addi, S. Adly, B. Brogliato, and D. Goeleven, A method using the appproach of Moreau and Panagiotopoulos for the mathematical formulation of non-regular circuits in electronics, Nonlinear Analysis: Hybrid Systems, vol.1, pp.30-43, 2007.

K. Addi, S. Adly, and H. Saoud, Finite-time Lyapunov stability analysis of evolution variational inequalities, Discrete and Continuous Dynamical Systems -Series A, vol.31, pp.1023-1038, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00683032

K. Addi, B. Brogliato, and D. Goeleven, A qualitative mathematical analysis of a class of linear variational inequalities via semi-complementarity problems. Applications in electronics, Mathematical Programming A, vol.126, pp.31-67, 2011.

K. Addi and D. Goeleven, Complementarity and variational inequalities in electronics, vol.113, pp.1-43, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01496877

S. Adly, Attractivity theory for second order nonsmooth dynamical systems with application to dry friction, Journal of Mathematical Analysis and Applications, vol.322, pp.1055-1070, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00450953

S. Adly, A Variational Approach to Nonsmooth Dynamics, Applications in Unilateral Mechanics and Electronics, 2017.
URL : https://hal.archives-ouvertes.fr/hal-02386068

S. Adly, A coderivative approach to the robust stability of composite parametric variational systems: applications in nonsmooth mechanics, Journal of Optimization Theory and Applications, vol.180, pp.62-90, 2019.
URL : https://hal.archives-ouvertes.fr/hal-02109951

S. Adly, H. Attouch, and A. Cabot, Kluwer, 2006, ch. Finite time stabilization of nonlinear oscillators subject to dry friction, Adv. in Math. and Mech, pp.289-304

S. Adly, B. Brogliato, and B. Le, Well-posedness, robustness and stability analysis of a set-valued controller for Lagrangian systems, SIAM Journal on Control and Optimization, vol.51, pp.1592-1614, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00825578

S. Adly and R. Cibulka, Quantitative stability of a generalized equation. application to nonregular electrical circuits, Journal of Optimization Theory and Applications, vol.160, pp.90-110, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00919288

S. Adly, R. Cibulka, and H. Massias, Variational analysis and generalized equations in electronics. Stability and simulation issues, Set Valued and Variational Analysis, vol.21, pp.333-358, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00880703

S. Adly and D. Goeleven, A stability theory for second-order nonsmooth dynamical systems with application to friction problems, Journal de Mathématiques Pures et Appliquées, vol.83, pp.17-51, 2004.
URL : https://hal.archives-ouvertes.fr/hal-00068291

S. Adly, D. Goeleven, and B. Le, Stability analysis and attractivity results of a DC-DC buck converter, Set Valued and Variational Analysis, vol.20, pp.331-353, 2012.

S. Adly, D. Goeleven, and M. Théra, Periodic solutions of evolution variational inequalities-a method of guiding functions, Chinese Annals of Mathematics, Series B, vol.30, pp.261-272, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00435716

S. Adly and T. Haddad, An implicit sweeping process approach to quasistatic evolution variational inequalities, SIAM Journal on Mathematical Analysis, vol.50, pp.761-778, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01710102

S. Adly and T. Haddad, On evolution quasi-variational inequalities and implicit statedependent sweeping processes, Discrete and Continuous Dynamical Systems Series S, 2019.

S. Adly and T. Haddad, Well-posedness of nonconvex degenerate sweeping process via unconstrained evolution problems, Nonlinear Analysis: Hybrid Systems, p.36, 2020.
URL : https://hal.archives-ouvertes.fr/hal-02386008

S. Adly, T. Haddad, and B. Le, State-dependent implicit sweeping process in the framework of quasistatic evolution quasi-variational inequalities, Journal of Optimization Theory and Applications, vol.182, pp.473-493, 2019.
URL : https://hal.archives-ouvertes.fr/hal-02386012

S. Adly, T. Haddad, and L. Thibault, Convex sweeping process in the framework of measure differential inclusions and evolution variational inequalities, Mathematical Programming B, vol.148, pp.5-47, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01313119

S. Adly, A. Hantoute, and B. Le, Nonsmooth Lur'e dynamical systems in Hilbert spaces, Set-Valued and Variational Analysis, vol.24, pp.13-35, 2016.

S. Adly, A. Hantoute, and B. Le, Maximal monotonicity and cyclic-monotonicity arising in nonsmooth Lur'e dynamical systems, Journal of Mathematical Analysis and Applications, vol.448, pp.691-706, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01656064

S. Adly, A. Hantoute, and B. Nguyen, Invariant sets and Lyapunov pairs for differential inclusions with maximal monotone operators, Journal of Mathematical Analysis and Applications, vol.457, pp.1017-1037, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01710076

S. Adly, A. Hantoute, and B. Nguyen, Equivalence between differential inclusions involving prox-regular sets and maximal monotone operators, 2018.

S. Adly, A. Hantoute, and B. Nguyen, Lyapunov stability of differential inclusions with Lipschitz Cusco perturbations of maximal monotone operators, Set-Valued and Variational Analysis, 2018.

S. Adly, A. Hantoute, and B. Nguyen, Lyapunov stability of differential inclusions involving prox-regular sets via maximal monotone operators, Journal of Optimization Theory and Applications, vol.182, pp.906-934, 2019.
URL : https://hal.archives-ouvertes.fr/hal-02386010

S. Adly, A. Hantoute, and M. Théra, Nonsmooth Lyapunov pairs for infinite-dimensional first-order differential inclusions, Nonlinear Analysis, vol.75, pp.985-1008, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00586942

S. Adly, A. Hantoute, and M. Théra, Nonsmooth Lyapunov pairs for differential inclusions governed by operators with nonempty interior domain, Mathematical Programming, vol.157, pp.349-374, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01313160

S. Adly and B. Le, Stability and invariance results for a class of non-monotone set-valued Lur'e dynamical systems, Applicable Analysis, vol.5, pp.1087-1105, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00919090

S. Adly and B. Le, Unbounded second-order state-dependent Moreau's sweeping processes in Hilbert spaces, Journal of Optimization Theory and Applications, vol.169, pp.407-423, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01313642

S. Adly and B. Le, Non-convex sweeping processes involving maximal monotone operators, Optimization, pp.1465-1486, 2017.

S. Adly and B. Le, On semicoercive sweeping process with velocity constraint, Optimization Letters, vol.12, pp.831-843, 2018.
URL : https://hal.archives-ouvertes.fr/hal-02386016

S. Adly and F. Nacry, An existence result for discontinuous second-order nonconvex statedependent sweeping processes, Applied Mathematics and Optimization, 2019.
URL : https://hal.archives-ouvertes.fr/hal-02109884

S. Adly, F. Nacry, and L. Thibault, Preservation of prox-regularity of sets and application to constrained optimization, SIAM Journal on Optimization, vol.26, pp.448-473, 2016.

S. Adly, F. Nacry, and L. Thibault, Discontinuous sweeping process with prox-regular sets, ESAIM: Control, Optimisation and Calculus of Variations, vol.23, pp.1293-1329, 2017.

D. Affane and M. Yarou, Unbouded perturbation for a class of variational inequalities, Discussiones Mathematicae, Differential Inclusions, Control and Optimization, vol.37, pp.83-99, 2017.

M. Aizerman and E. Pyatnitskii, Foundation of a theory of discontinuous systems I, Automation and Remote Control, Avtom. Telemekh.), vol.7, pp.33-47, 1974.

M. Aizerman and E. Pyatnitskii, Foundation of a theory of discontinuous systems II, Automation and Remote Control, Avtom. Telemekh.), vol.8, pp.39-61, 1974.

F. Aliouane, D. Azzam-laouir, C. Castaing, and M. Monteiro-marques, Second-order and state-dependent sweeping process in Hilbert space, Journal of Optimization Theory and Applications, vol.182, pp.153-188, 2019.

F. Aliouane and F. Azzam-laouir, Second order sweeping process with a Lipschitz perturbation, Journal of Mathematical Analysis and Applications, vol.452, pp.729-746, 2017.

F. Alvarez, On the minimizing property of a second order dissipative system in Hilbert spaces, SIAM Journal on Control and Optimization, vol.38, pp.1102-1119, 2000.

F. Alvarez and H. Attouch, An inertial proximal method for maximal monotone operators via discretization of a nonlinear oscillator with damping, Set-Valued Analysis, vol.9, pp.3-11, 2001.

J. Alvarez, I. Orlov, and L. Acho, An invariance principle for discontinuous dynamic systems with applications to a Coulomb friction oscillator, Transactions ASME J. Dynam. Systems Measurement Control, vol.122, pp.687-690, 2000.

N. Amundson, A. Caboussat, J. He, C. Landry, and J. Seinfled, A dynamic optimization problem related to organic aerosols, C.R. Acad. Scio. paris Ser. I, vol.344, pp.519-522, 2007.

B. Anderson and P. Moylan, Synthesis of linear time-varying passive networks, IEEE Transactions on Circuits and Systems, vol.21, pp.678-687, 1974.

A. Antipin, Minimization of convex functions on convex sets by means of differential equations, Russian Differentsial'nye Uravneniya, Translated in Differential Equations, vol.30, issue.9, pp.1365-1375, 1994.

C. Arroud and G. Colombo, A maximum principle for the controlled sweeping process, Set-Valued Var, Anal, vol.26, pp.607-629, 2018.

H. Attouch, A. Cabot, and M. Czarnecki, Asymptotic behavior of nonautonomous monotone and subgradient evolution equations, Transactions of the American Mathematical Society, vol.370, pp.755-790, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01660954

H. Attouch and M. Czarnecki, Asymptotic behaviour of coupled dynamical systems with multiscale aspects, J. of Differential Equations, vol.248, pp.1315-1344, 2010.

H. Attouch and J. Peypouquet, Convergence of inertial dynamics and proximal algorithms governed by maximally monotone operators, Mathematical Programming series B, vol.174, 2019.
URL : https://hal.archives-ouvertes.fr/hal-01821953

H. Attouch, J. Peypouquet, and P. Redont, A dynamical approach to an inertial forwardbackward algorithm for convex minimization, SIAM Journal on Optimization, vol.24, pp.232-256, 2014.
URL : https://hal.archives-ouvertes.fr/hal-02072843

H. Attouch, J. Peypouquet, and P. Redont, Fast convex optimization via inertial dynamics with Hessian driven damping, Journal of Differential Equations, vol.261, pp.5734-5783, 2016.
URL : https://hal.archives-ouvertes.fr/hal-02072674

H. Attouch and B. Svaiter, A continuous dynamical Newton-like approach to solving monotone inclusions, SIAM Journal on Control and Optimization, vol.49, pp.574-598, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00803137

J. Aubin, Viability Theory, Systems and Control: Foundations and Applications, 1991.

J. Aubin and A. Cellina, Differential Inclusions: Set-Valued Maps and Viability, 1984.

J. Aubin and H. Frankowska, Set-Valued Analysis, 1990.

D. Azzam-laouir, W. Belhoula, C. Castaing, and M. Monteiro-marques, Multi-valued perturbation to evolution problems involving time dependent maximal monotone operators, Evolution Equations and Control Theory, vol.9, pp.219-254, 2020.

D. Azzam-laouir, C. Castaing, and M. Monteiro-marques, Perturbed evolution problems with continuous bounded variation in time and applications, Set-Valued Var, Anal, vol.26, pp.693-728, 2018.

D. Azzam-laouir and S. Izza, Existence of solutions for second-order perturbed nonconvex sweeping process, Computers in Mathematics with Applications, vol.62, pp.1736-1744, 2011.

D. Azzam-laouir, S. Izza, and L. Thibault, Mixed semicontinuous perturbation of nonconvex state-dependent sweeping process, Set-Valued and Variational Analysis, vol.22, pp.271-283, 2017.

V. Babitsky, Theory of Vibro-Impact Systems and Applications, Foundations of Engineering Mechanics, 1998.

A. Bacciotti, F. Ceragioli, and L. Mazzi, Differential inclusions and monotonicity conditions for nonsmooth Liapunov functions, Set-Valued Analysis, vol.8, pp.299-309, 2000.

A. Bacciotti and L. Rosier, Liapunov Functions and Stability in Control Theory, Communications and Control Engineering, 2005.

F. Bagagiolo, Dynamic programming for some optimal control problems with hysteresis, Nonlinear Differential Equations and Applications NoDEA, vol.9, pp.149-174, 2002.

B. Baji and A. Cabot, An inertial proximal algorithm with dry friction: finite convergence results, Set Valued Analysis, vol.14, pp.1-23, 2006.

P. Ballard, The dynamics of discrete mechanical systems with perfect unilateral constraints, Archive for Rational Mechanics and Analysis, vol.154, pp.199-274, 2000.

P. Ballard, Formulation and well-posedness of the dynamics of rigid body systems with perfect unilateral constraints, Phil. Trans. R. Soc. Lond. A, vol.359, pp.2327-2346, 2001.
URL : https://hal.archives-ouvertes.fr/hal-01722467

P. Ballard and S. Basseville, Existence and uniqueness for dynamical unilateral contact with Coulomb friction: a model problem, ESAIM: Mathematical Modelling and Numerical Analysis, vol.39, issue.M2AN, pp.59-77, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00461828

P. Ballard, A. Léger, and E. Pratt, Stability of discrete systems involving shocks and friction, in Analysis and Simulation of Contact Problems, Lecture Notes in Applied and Computational Mechanics, pp.343-350, 2006.

X. Ban, H. Liu, M. Ferris, and B. Ran, A link-node complementarity model and solution algorithm for dynamic user equilibria with exact propagations, Transportation Research Part B, vol.42, pp.823-842, 2008.

X. Ban, J. Pang, H. Liu, and R. Ma, Continuous-time point-queue models in dynamic network loading, Transportation Research Part B, vol.46, pp.360-380, 2012.

X. Ban, J. Pang, H. Liu, and R. Ma, Modeling and solving continuous-time instantaneous dynamic user equilibria: A differential complementarity systems approach, Transportation Research Part B, vol.46, pp.389-408, 2012.

N. Barabanov and V. Yakubovich, Absolute stability of control systems with one hysteresis nonlinearity, Automation and Remote Control, vol.12, pp.5-12, 1979.

P. Barton, K. Khan, P. Stechlinski, and H. Watson, Computationally relevant generalized derivatives: theory, evaluation and applications, Optimization Methods and Software, vol.33, pp.1030-1072, 2018.

S. Basseville and A. Léger, Stability of equilibrium states in a simple system with unilateral contact and Coulomb friction, Archive of Applied Mechanics, vol.76, pp.403-428, 2006.
URL : https://hal.archives-ouvertes.fr/hal-01310671

S. Basseville, A. Léger, and E. Pratt, Investigation of the equilibrium states and their stability for a simple model with unilateral contact and Coulomb friction, Archive of Applied Mechanics, vol.73, pp.409-420, 2003.
URL : https://hal.archives-ouvertes.fr/hal-00088347

J. Bastien, Convergence order of implict Euler numerical scheme for maximal monotone differential inclusions, Z. Angew. Math. Phys, vol.64, pp.955-966, 2013.

J. Bastien, Study of a driven and braked wheel using maximal monotone differential inclusions: applications to the nonlinear dynamics of wheeled vehicles, Archive of Applied Mechanics, vol.84, pp.851-880, 2014.

J. Bastien, F. Bernardin, and C. Lamarque, Systèmes Dynamiques Discrets Non Réguliers Déterministes ou Stochastiques, 2012.

J. Bastien and C. Lamarque, Persoz's gephyroidal model described by a maximal monotone differential inclusion, Archive of Applied Mechanics, vol.78, pp.393-407, 2008.

J. Bastien and C. Lamarque, Maximal monotone model with history term, Nonlinear Analysis, vol.63, pp.199-207, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00814984

J. Bastien and C. Lamarque, Theoretical study of a chain sliding on a fixed support, Mathematical Problems in Engineering, pp.1-19, 2009.

J. Bastien, G. Michon, L. Manin, and R. Dufour, An analysis of the modified Dahl and Masing models: application to a belt tensioner, Journal of Sound and Vibration, vol.302, pp.841-864, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00380794

J. Bastien, M. Schatzman, and C. Lamarque, Study of some rheological models with a finite number of degrees of freedom, European Journal of Mechanics A/Solids, vol.19, pp.277-307, 2000.
URL : https://hal.archives-ouvertes.fr/hal-00814948

J. Bastien, M. Schatzman, and C. Lamarque, Study of an elastoplastic model with an infinite number of internal degrees of freedom, European Journal of Mechanics A/Solids, vol.21, pp.199-222, 2002.
URL : https://hal.archives-ouvertes.fr/hal-00814955

C. Batlle, E. Fossas, I. Merillas, and A. Miralles, Generalized discontinuous conduction modes in the complementarity formalism, IEEE Transactions on Circuits and Systems-II: Express Briefs, vol.52, pp.447-451, 2005.

M. Baumann, J. Biemond, R. Leine, and N. Van-de-wouw, Synchronization of impacting systems with a single constraint, Physica D, vol.362, pp.9-23, 2018.

M. Baumann and R. Leine, A synchronization-based state observer for impact oscillators using only collision time information, Int. Journal of Robust and Nonlinear Control, vol.26, pp.2542-2563, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01326052

B. Baumrucker and L. Biegler, MPEC strategies for optimization of a class of hybrid dynamic systems, Journal of Process Control, vol.19, pp.1248-1256, 2009.

H. Bauschke and P. Combettes, Convex Analysis and Monotone Operator Theory in Hilbert Spaces, Canadian Mathematical Society Books in Mathematics, 2011.
URL : https://hal.archives-ouvertes.fr/hal-01517477

C. Behn, Adaptive control of straight worms without derivative measurement, Multibody System Dynamics, vol.26, pp.213-243, 2011.

H. Benabdellah, Existence of solutions to the nonconvex sweeping process, Journal of Differential Equations, vol.164, pp.286-295, 2000.

H. Benabdellah and A. Faik, Perturbations convexes et non convexes deséquations d'évolution, vol.53, pp.187-208, 1996.

A. Benveniste, T. Bourke, B. Caillaud, and M. Pouzet, Non-standard semantics of hybrid systems modelers, Journal of Computer and System Sciences, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00766726

F. Bernard and L. Thibault, Uniform prox-regularity of functions and epigraphs in Hilbert spaces, Nonlinear Analysis: Theory, Methods and Applications, vol.60, pp.187-207, 2005.

F. Bernicot and J. Venel, Stochastic perturbation of sweeping process and a convergence result for an associated numerical scheme, Journal of Differential Equations, pp.1195-1224, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00448064

D. Bernstein, Matrix Mathematics. Theory, facts, and Formulas with Application to Linear Systems Theory, 2005.

P. Bettiol, A deterministic approach to the Skorokhod problem, Control and Cybernetics, vol.35, pp.787-801, 2006.

W. Bian and X. Xue, Evolution differential inclusion with projection for solving constrained nonsmooth convex optimization in Hilbert space, Set-Valued Var. Anal, vol.20, pp.203-227, 2012.

J. Biemond, W. Michiels, and N. Van-de-wouw, Stability analysis of equilibria of linear delay complementarity systems, IEEE Control Systems Letters, vol.1, pp.158-163, 2017.

A. Bisoffi, M. D. Lio, A. Teel, and L. Zaccarian, Global asymptotic stability of a PID control system with Coulomb friction, IEEE Transactions on Automatic Control, vol.63, pp.2654-2661, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01700168

A. Blumentals, B. Brogliato, and F. Bertails-descoubes, The contact problem in Lagrangian systems subject to bilateral and unilateral constraints, with or without sliding Coulomb's friction: A tutorial, Multibody System Dynamics, vol.38, pp.43-76, 2016.

I. Boiko, Oscillations and transfer properties of relay servo systems-the locus of a perturbed relay system approach, Automatica, pp.677-683, 2005.

J. Bolte, Continuous gradient projection method in Hilbert spaces, Journal of Optimizaton Theory and Applications, vol.119, pp.235-259, 2003.

R. Bot and E. Csetnek, Approaching nonsmooth nonconvex optimization problems thourgh first order dynamical systems with hidden acceleration and Hessian damping terms, Set-Valued Var, Anal, vol.26, pp.227-245, 2018.

M. Bounkhel, Existence results for nonconvex differential inclusions, Portugaliae Matematica, vol.59, pp.283-309, 2002.

M. Bounkhel, Existence and uniqueness of some variants of nonconvex sweeping processes, Journal of Nonlinear and Convex Analysis, vol.8, pp.311-323, 2007.

M. Bounkhel and D. Azzam-laouir, Existence results on the second-order nonconvex sweeping processes with perturbations, Set-Valued Var, Anal, vol.12, pp.291-318, 2004.

M. Bounkhel and L. Thibault, Nonconcex sweeping process and prox-regularity in Hilbert space, Journal of Nonlinear and Convex Analysis, vol.6, pp.359-374, 2001.

M. Bounkhel and M. Yarou, Existence results for first and second order nonconvex sweeping process with delay, Portugaliae Mathematica, pp.207-230, 2004.

J. Bourgeot and B. Brogliato, Tracking control of Lagrangian complementarity systems, International Journal of Bifurcation and Chaos, vol.15, pp.1839-1866, 2005.
URL : https://hal.archives-ouvertes.fr/inria-00070619

Y. Brenier, W. Gangbo, G. Savaré, and M. Westdickenberg, Sticky particle dynamics with interactions, pp.577-617, 2013.

A. Bressan, Incompatbilita dei teoremi di esistenza e di unicita del moto per un tipo molto comune e regolare di sistemi meccanici, Annali della Scuola Normale Superiore di Pisa, Classe di Scienze 3e série, vol.14, pp.333-348, 1959.

A. Bressan, A. Cellina, and G. Colombo, Upper semicontinuous differential inclusions without convexity, Proceedings of the American Mathematcal Society, vol.186, pp.771-775, 1989.

A. Bressan, M. Mazzola, and K. Nguyen, Approximation of sweeping processes and controllability for a set-valued evolution, SIAM Journal on Control and Optimization, vol.57, pp.2487-2514, 2019.

H. Brezis, Opérateurs Maximaux Monotones et Semi-Groupes de Contraction dans les Espaces de Hilbert, 1973.

L. Briceno-arias, N. Hoang, and J. Peypouquet, Existence, stability and optimality for optimal control problems governed by maximal monotone operators, Journal of Differential Equations, vol.260, pp.733-757, 2016.

B. Brogliato, Some perspectives on the analysis and control of complementarity systems, IEEE Transactions on Automatic Control, vol.48, pp.918-935, 2003.
URL : https://hal.archives-ouvertes.fr/hal-01660014

B. Brogliato, Absolute stability and the Lagrange-Dirichlet theorem with monotone multivalued mappings, Systems and Control Letters, vol.51, pp.343-353, 2004.
URL : https://hal.archives-ouvertes.fr/inria-00071792

B. Brogliato, Some results on the controllability of planar evolution variational inequalities, Systems and Control Letters, vol.54, pp.65-71, 2005.

B. Brogliato, Some results on the optimal control with unilateral state constraints, Nonlinear Analysis: Theory, Methods and Applications, vol.70, pp.3626-3657, 2009.
URL : https://hal.archives-ouvertes.fr/inria-00103775

B. Brogliato, Inertial couplings between unilateral and bilateral holonomic constraints in frictionless Lagrangian systems, Multibody System Dynamics, vol.29, pp.289-325, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00825581

B. Brogliato, Nonsmooth Mechanics. Models, Dynamics and Control

B. Brogliato, Feedback control of multibody systems with joint clearance and dynamic backlash: a tutorial, Multibody System Dynamics, vol.42, pp.283-315, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01499581

B. Brogliato, Non-autonomous higher-order Moreau's sweeping process: Well-posedness, stability and Zeno trajectories, European Journal of Applied Mathematics, vol.29, pp.941-968, 2018.

B. Brogliato, A. Daniilidis, C. Lemaréchal, and V. Acary, On the equivalence between complementarity systems, projected systems and differential inclusions, Systems and Control Letters, vol.55, pp.45-51, 2006.

B. Brogliato and D. Goeleven, The Krasovskii-LaSalle invariance principle for a class of unilateral dynamical systems, Mathematics of Control, Signals and Systems, vol.17, pp.57-76, 2005.

B. Brogliato and D. Goeleven, Well-posedness, stability and invariance results for a class of multivalued Lur'e dynamical systems, Nonlinear Analysis: Theory, Methods and Applications, vol.74, pp.195-212, 2011.
URL : https://hal.archives-ouvertes.fr/hal-01633239

B. Brogliato and D. Goeleven, Existence, uniqueness of solutions and stability of nonsmooth multivalued Lur'e dynamical systems, Journal of Convex Analysis, vol.20, pp.881-900, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00825601

B. Brogliato and D. Goeleven, Singular mass matrix and redundant constraints in unilaterally constrained Lagrangian and Hamiltonian systems, Multibody System Dynamics, vol.35, pp.39-61, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01088286

B. Brogliato and W. Heemels, Observer design for Lur'e systems with multivalued mappings: a passivity approach, IEEE Transactions on Automatic Control, vol.54, pp.1996-2001, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00756302

B. Brogliato, R. Lozano, B. Maschke, and O. Egeland, Dissipative Systems Analysis and Control, Communications and Control Engineering, 2020.
URL : https://hal.archives-ouvertes.fr/hal-00821748

B. Brogliato, M. Mabrouk, and A. Z. Rio, On the controllability of linear juggling mechanical systems, Systems and Control Letters, vol.55, pp.350-367, 2006.
URL : https://hal.archives-ouvertes.fr/hal-02303983

B. Brogliato, S. Niculescu, and M. Monteiro-marques, On tracking control of a class of complementary-slackness hybrid mechanical systems, Systems and Control Letters, vol.39, pp.255-266, 2000.
URL : https://hal.archives-ouvertes.fr/hal-02299338

B. Brogliato, S. Niculescu, and P. Orhant, On the control of finite-dimensional mechanical systems with unilateral constraints, IEEE Transactions on Automatic Control, vol.42, pp.200-215, 1997.

B. Brogliato and L. Thibault, Existence and uniqueness of solutions for non-autonomous complementarity dynamical systems, Journal of Convex Analysis, vol.17, pp.961-990, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00756226

M. Brokate and P. Krejci, Optimal control of ODE systems involving a rate independent variational inequality, Discrete and Continuous Dynamical Systems -Series B, vol.18, pp.331-348, 2013.

C. Byrnes and A. Isidori, Asymptotic stabilization of minimum phase nonlinear systems, IEEE Transactions on Automatic Control, vol.36, pp.1122-1337, 1991.

A. Cabot, Stabilization of oscillators subject to dry friction: finite time convergence versus exponential decay results, Transactions of the American Mathematical Society, vol.360, pp.103-121, 2008.

A. Cabot and L. Paoli, Asymptotics for some vibro-impact problem with linear dissipation term, Journal de Mathématiques Pures et Appliquées, vol.87, pp.291-323, 2007.

A. Caboussat and C. Landry, A second order scheme for solving optimization-constrained differential equations with discontinuities, Proceedings of ENUMATH07, the 7th European Conference on Numerical Mathematics and Advanced Applications, pp.761-768, 2008.

M. Camlibel, Complementarity Methods in the Analysis of Piecewise Linear Dynamical Systems, vol.90, p.73, 2001.

M. Camlibel, Popov-Belevitch-Hautus type tests for the controllability of linear complementarity systems, Systems and Control Letters, vol.56, pp.381-387, 2007.

M. Camlibel, W. Heemels, and J. Schumacher, On linear passive complementarity systems, European Journal of Control, vol.8, pp.220-237, 2002.

M. Camlibel, W. Heemels, A. Van-der-schaft, and J. Schumacher, Switched networks and complementarity, IEEE Transactions on Circuits and Systems I, vol.50, pp.1036-1048, 2003.

M. Camlibel, L. Iannelli, and A. Tanwani, Convergence of proximal solutions for evolution inclusions with time-dependent maximal monotone operators, 2019.
URL : https://hal.archives-ouvertes.fr/hal-02144478

M. Camlibel, L. Iannelli, A. Tanwani, and S. Trenn, Differential-algebraic inclusions with maximal monotone operators, 55th IEEE Conference on Decision and Control, pp.610-615, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01366071

M. Camlibel, L. Iannelli, and F. Vasca, Passivity and complementarity, vol.145, pp.531-563, 2014.

M. Camlibel, J. Pang, and J. Shen, Conewise linear systems: non-Zenoness and observability, SIAM Journal on Optimization, vol.17, pp.1056-1101, 2006.

M. Camlibel, J. Pang, and J. Shen, Lyapunov stability of complementarity and extended systems, SIAM Journal on Optimization, vol.17, pp.1056-1101, 2006.
URL : https://hal.archives-ouvertes.fr/hal-01970624

M. Camlibel and J. Schumacher, Copositive Lyapunov functions, Unsolved Problems in Mathematical Systems and Control Theory, pp.189-193, 2004.

M. Camlibel and J. Schumacher, Linear passive systems and maximal monotone mappings, Mathematical Programming B, vol.157, pp.397-420, 2016.

T. Cao and B. Mordukhovich, Optimal control of a perturbed sweeping process via discrete approximations, Disc. Cont. Dyn. Syst. Ser. B, vol.21, pp.3331-3358, 2016.

T. Cao and B. Mordukhovich, Optimal control of a nonconvex perturbed sweeping process, 2017.

T. Cao and B. Mordukhovich, Optimality conditions for a controlled sweeping process with applications to the crowd motion model, Disc. Cont. Dyn. Syst. Ser. B, vol.22, pp.267-306, 2017.

S. Carl, V. Le, and D. Motreanu, Nonsmooth Variational Problems and Their Inequalities. Comparison Principles and Applications, 2007.

A. Carta, M. Chaves, and J. Gouzé, Continuous-switch piecewise quadratic models of biological networks: Application to bacterial growth, Automatica, pp.164-172, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01231368

R. Casey, H. D. Jong, and J. Gouzé, Piecewise-linear models of genetic regulatory networks: Equilibria and their stability, Journal of Mathematical Biology, vol.52, pp.27-56, 2006.
URL : https://hal.archives-ouvertes.fr/inria-00071250

C. Castaing, Version aléatoire de problème de rafle par un convexe variable, C.R. Acad. Sci. Paris, Série A, vol.277, pp.1057-1059, 1973.

C. Castaing, Rafle par un convexe aléatoireà variation continuè a droite, C.R. Acad. Sci. Paris, Série A, vol.282, pp.515-518, 1976.

C. Castaing, Quelques problèmes d'évolution du second ordre, Séminaire d'Analyse Convexe, 1988.

C. Castaing, T. Ha, and M. Valadier, Evolution equations governed by the sweeping process, Set-Valued Analysis, vol.1, pp.109-139, 1993.

C. Castaing, A. Ibrahim, and M. Yarou, Some contributions to nonconvex sweeping process, Journal of Nonlinear and Convex Analysis, vol.10, pp.1-20, 2009.

C. Castaing, A. Ibrahim, and M. Yarou, Existence problems in second order evolution inclusions: discretization and variational approach, Taiwanese Journal of Mathematics, vol.12, pp.1435-1477, 2008.

C. Castaing and M. , Monteiro-Marques, BV periodic solutions of an evolution problem associated with continuous moving convex sets, Set-Valued Analysis, vol.3, pp.381-399, 1995.

C. Castaing and M. Monteiro-marques, Periodic solutions of an evolution problems associated with a moving convex sets, C.R. Acad.Sci. Paris Ser. A, vol.321, pp.531-536, 1995.

C. Castaing and M. Monteiro-marques, Topological properties of solution sets for sweeping processes with delay, Portugaliae Mathematica, vol.54, pp.485-507, 1997.

C. Castaing, M. Monteiro-marques, and P. R. De-fitte, Some problems in optimal control governed by the sweeping process, Journal of Nonlinear and Convex Analysis, vol.15, pp.1043-1070, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01074043

C. Castaing, M. Monteiro-marques, and P. R. De-fitte, A Skorokhod problem governed by a closed convex moving set, Journal of Convex Analysis, vol.23, pp.387-423, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01780957

C. Castaing, A. Salvadori, and L. Thibault, Functional evolution equations governed by nonconvex sweeping process, Journal of Nonlinear and Convex Analysis, vol.2, pp.217-241, 2001.

E. Cavazzuti, M. Pappalardo, and M. Passacantando, Nash equilibria, variational inequalities, and dynamical systems, Journal of Optimization Theory and Applications, vol.114, pp.491-506, 2002.

A. Cellina and V. Staicu, On evolution equations having monotonicities of opposite sign, Journal of Differential Equations, vol.90, pp.71-80, 1991.

F. Ceragioli, C. De-persis, and P. Frasca, Discontinuities and hysteresis in quantized average consensus, Automatica, vol.47, pp.1916-1928, 2011.

F. Ceragioli and P. Frasca, Consensus and disagreement: The role of quantized behaviors in opinion dynamics, SIAM Journal on Control and Optimization, vol.56, pp.1056-1080, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01741358

A. Champneys and P. Varkonyi, The Painlevé paradox in contact mechanics, IMA Journal of Applied Mathematics, vol.81, pp.538-588, 2016.

P. Champsaur, J. Drèze, and C. Henry, Stability theorems with economic applications, Econometrica, vol.45, pp.273-294, 1977.

X. Chateau and Q. Nguyen, Buckling of elastic structures in unilateral contact, European Journal of Mechanics, A/Solids, vol.10, pp.71-89, 1991.
URL : https://hal.archives-ouvertes.fr/hal-00105477

M. Chaves and J. Gouzé, Exact control of genetic networks in a qualitative framework: The bistable switch example, Automatica, vol.47, pp.1105-1112, 2011.
URL : https://hal.archives-ouvertes.fr/inria-00507040

N. Chemetov and M. Monteiro-marques, Non-convex quasi-variational differential inclusions, Set-Valued and Variational Analysis, vol.15, pp.209-221, 2007.

D. Chen, G. Yang, and Z. Han, Impulsive observer for input-to-state stability based synchronization of Lur'e differential inclusion system, Communications in Nonlinear Science and Numerical Simulation, vol.17, pp.2990-2996, 2012.

X. Chen and Z. Wang, Differential variational inequality approach to dynamic games with shared constraints, Mathematical Programming A, vol.146, pp.379-408, 2014.

A. Cherukuri, E. Mallada, and J. Cortès, Asymptotic convergence of constrained primaldual dynamics, Systems and Control Letters, vol.87, pp.10-15, 2016.

A. Cherukuri, E. Mallada, S. Low, and J. Cortès, The role of convexity in saddle-point dynamics: Lyapunov function and robustness, IEEE Transactions on Automatic Control, vol.109, pp.2449-2464, 2018.

F. Clarke, Y. Ledyaev, R. Stern, and P. Wolenski, Nonsmooth Analysis and Control Theory, 1998.
URL : https://hal.archives-ouvertes.fr/hal-00863298

M. Cojocaru, Monotonicity and existence of periodic orbits for projected dynamical systems on Hilbert spaces, Proceedings of the American Mathematical Society, vol.134, pp.793-804, 2005.

M. Cojocaru, Dynamic equilibria of group vaccination strategies in a heterogeneous population, J. Global Optimization, vol.40, pp.51-63, 2008.

M. Cojocaru, C. Bauch, and M. Johnston, Dynamics of vaccination strategies via projected dynamical systems, Bulletin of Mathematical Biology, vol.69, pp.1453-1476, 2007.

M. Cojocaru, P. Daniele, and A. Nagurney, Projected dynamical systems and evolutionary variational inequalities via Hilbert spaces with applications, Journal of Optimization Theory and Applications, vol.127, pp.549-563, 2005.

M. Cojocaru, P. Daniele, and A. Nagurney, Double-layered dynamics: A unified theory of projected dynamical systems and evolutionary variational inequalities, European Journal of Operational Research, vol.175, pp.494-507, 2006.

M. Cojocaru and L. Jonker, Existence of solutions to projected differential equations in Hilbert spaces, Proceedings of the American Mathematical Society, vol.132, pp.183-193, 2004.

P. Colli, P. Krejci, E. Rocca, and J. Sprekels, Nonlinear evolution inclusions arising from phase change models, Czechoslovak Mathematical Journal, vol.57, pp.1067-1098, 2007.

G. Colombo and V. Goncharov, The sweeping process without convexity, Set-Valued Analysis, vol.7, pp.357-374, 1999.

G. Colombo, R. Henrion, D. Hoang, and S. Mordukhovich, Optimal control of the sweeping process, Dyn. Contin. Discrete Impuls. Syst. Ser. B Appl. Algorithms, vol.19, pp.117-159, 2012.

G. Colombo, R. Henrion, D. Hoang, and S. Mordukhovich, Discrete approximations of a controlled sweeping process, Set-Valued and Variational Analysis, vol.23, pp.69-86, 2015.

G. Colombo, R. Henrion, D. Hoang, and S. Mordukhovich, Optimal control of the sweeping process over polyhedral controlled sets, Journal of Differential Equations, vol.260, pp.3397-3447, 2016.

G. Colombo and C. Kozaily, Existence and uniqueness of solutions for an integral perturbation of Moreau's sweeping process, Journal of Convex Analysis, p.27, 2020.

G. Colombo and M. Monteiro-marques, Sweeping by a continuous prox-regular set, Journal of Differential Equations, vol.187, pp.46-62, 2003.

G. Colombo, B. Mordukhovich, and D. Nguyen, Optimal control of sweeping processes in robotics and traffic flow models, Journal of Optimization Theory and Applications, vol.182, pp.439-472, 2019.

G. Colombo, B. Mordukhovich, and D. Nguyen, Optimization of a perturbed sweeping process by constrained discontinuous controls, SIAM Journal on Control and Optimization, 2020.

G. Colombo and M. Palladino, The minimum time function for the controlled Moreau's sweeping process, SIAM Journal on Control and Optimization, vol.54, pp.2036-2052, 2016.

P. Combettes and J. Pesquet, Proximal splitting methods in signal processing, Inverse Problems in Science and Engineering, vol.49, pp.185-212, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00643807

B. Cornet, Existence of slow solutions for a class of differential inclusions, Journal of Mathematical Analysis and Applications, vol.96, pp.130-147, 1983.

R. Cottle, J. Pang, and R. Stone, The Linear Complementarity Problem, Computer Science and Scientific Computing, 1992.

P. Daniele, Variational inequalities for evolutionary financial equilibrium, Innovations in Financial and Economic Networks, New Dimensions in Networks, pp.84-108, 2003.

P. Daniele, Dynamic Networks and Evolutionary Variational Inequalities, New Dimensions in Networks, 2006.

P. Daniele, A. Maugeri, and W. Oettli, Variational inequalities and time-dependent traffic equilibria, Comptes Rendus Académie des Sciences Paris, pp.1059-1062, 1998.

P. Daniele, A. Maugeri, and W. Oettli, Time-dependent variational inequalities, Journal of Optimization Theory and Applications, vol.104, pp.543-555, 1999.

J. De-bruin, A. Doris, N. Van-de-wouw, W. Heemels, and H. Nijmeijer, Control of mechanical motion systems with non-collocation of actuation and friction: a Popov criterion approach for input-to-state stability and set-valued nonlinearities, Automatica, vol.45, pp.405-415, 2009.

H. Jong, J. Gouzé, C. Hernandez, M. Page, T. Sari et al., Qualitative simulation of genetic regulatory networks using piecewise-linear models, Bulletin of Mathematical Biology, vol.66, pp.301-340, 2004.
URL : https://hal.archives-ouvertes.fr/hal-00173849

M. De-pinho, M. Ferreira, and G. Smirnov, Optimal control involving sweeping processes, Set-Valued and Variational Analysis, vol.27, pp.523-548, 2019.

G. Sandre, M. Forti, P. Nistri, and A. Premoli, Dynamical analysis of full-range cellular neural networks by exploiting differential variational inequalities, IEEE Transactions on Circuits and Systems-I: Regular Papers, vol.54, pp.1736-1749, 2007.

G. De-saxcé and Z. Feng, The bipotential method: a constructive approach to design the complete contact law with friction and improved numerical algorithm, Math. Comput. Modelling, vol.28, pp.225-245, 1998.

K. Deimling, Multivalued Differential Equations, Nonlinear Analysis and Applications, 1992.

E. Delassus, Mémoire sur la théorie des liaisons finies unilatérales, Annales Scientifiques de l' Ecole Normale Supèrieure, vol.34, pp.95-179, 1917.

Z. Deng, X. Nian, and C. Hu, Distributed algorithm design for nonsmooth resource allocation problems, IEEE Transactions on Cybernetics, 2019.

N. Dhingra, S. Khong, and M. Jovanovic, The proximal augmented Lagrangian method for nonsmooth composite optimization, IEEE Transactions on Automatic Control, vol.64, pp.2861-2868, 2019.

M. Bernardo, C. Budd, A. Champneys, and P. Kowalczyk, Piecewise-smooth Dynamical Systems, Applied Mathematical Sciences, vol.163, 2008.

S. Di-marino, B. Maury, and F. Santambrogio, Measure sweeping processes, Journal of Convex Analysis, vol.23, pp.1923-2014, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01249493

L. Dieci and L. Lopez, Sliding motion on discontinuity surfaces of high co-dimension. A construction for selecting a Filippov vector field, Numerische Mathematik, vol.117, pp.779-811, 2011.

M. Dolgopolik and A. Fradkov, Nonsmooth and discontinuous speed-gradient algorithms, Nonlinear Analysis: Hybrid Systems, vol.25, pp.99-113, 2017.

J. Dong, D. Zhang, and A. Nagurney, A projected dynamical systems model of general financial equilibrium with stability analysis, Mathematical and Computer Modelling, vol.24, pp.35-44, 1996.

X. Dong and Y. Gao, The equivalence between a complementarity control system and a differential inclusion, International Journal of Nonlinear Science, vol.5, pp.106-110, 2008.

A. Doris, A. Juloski, N. Mihajlovic, W. Heemels, N. Van-de-wouw et al., Observer designs for experimental non-smooth and discontinuous systems, IEEE Transactions on Control Systems Technology, vol.16, pp.1323-1332, 2008.

B. Du and D. Wang, Continuum modelling of park-and-ride services considering travel time reliability and heterogeneous commuters-a linear complementarity system approach, Transportation Research Part E, vol.71, pp.58-81, 2014.

P. Dupuis and A. Nagurney, Dynamical systems and variational inequalities, Annals of Operations Research, vol.44, pp.9-42, 1993.

R. Dzonou and M. Monteiro-marques, A sweeping process approach to inelastic contact problems with general inertia operators, European Journal of Mechanics A/Solids, vol.26, pp.474-490, 2007.

R. Dzonou, M. Monteiro-marques, and L. Paoli, A convergence result for a vibroimpact problem with a general inertia operator, Nonlinear Dynamics, vol.58, pp.361-384, 2009.
URL : https://hal.archives-ouvertes.fr/hal-01552482

J. Edmond, Delay perturbed sweeping process, Set-Valued Analysis, vol.14, pp.295-317, 2006.

J. Edmond, Relaxation of a Bolza problem governed by a time-delay sweeping process, Set-Valued Analysis, vol.16, pp.563-580, 2008.

J. Edmond and L. Thibault, Relaxation of an optimal control problem involving a perturbed sweeping process, Mathematical Programming A, vol.104, pp.347-373, 2005.

J. Edmond and L. Thibault, BV solutions of nonconvex sweeping process differential inclusion with perturbation, Journal of Differential Equations, vol.226, pp.135-179, 2006.

G. Eichfelder and G. Jahn, Set-semidefinite optimization, Journal of Convex Analysis, vol.15, pp.767-801, 2008.

F. Facchinei and J. Pang, Finite-Dimensional Variational Inequalities and Complementarity Problems, Springer Series in Operations Research, vol.I, 2003.

L. A. Faik and A. Syam, Differential inclusions governed by a nonconvex sweeping process, Journal of Nonlinear and Convex Analysis, vol.2, pp.381-392, 2001.

M. Falcone and P. Saint-pierre, Slow and quasi-slow solutions of differential inclusions, Nonlinear Analysis: Theory, Methods and Applications, vol.11, pp.367-377, 1987.

H. Fatoorehchi, H. Abolghasemi, and R. Zarghami, Analytical approximate solutions for a general nonlinear resistor-nonlinear capacitor circuit model, Applied Mathematical Modelling, vol.39, pp.6021-6031, 2015.

D. Feijer and F. Paganini, Stability of primal-dual gradient dynamics and applications to network optimization, Automatica, vol.46, pp.1974-1981, 2010.

G. Feng and X. Tan, Absolute stability of a class of singular nonlinear systems with setvalued mappings, Systems, and Computers, vol.24, pp.1550015-1550016, 2015.

A. Ferrara and V. Utkin, Sliding mode optimization in dynamic LTI systems, Journal of Optimization Theory and Applications, vol.115, pp.727-740, 2002.

L. Ferreira, E. Kaszkurewicz, and A. Bhaya, Solving systems of linear equations via gradient systems with discontinuous righthand sides: application to LS-SVM, IEEE Transactions on Neural Networks, vol.16, pp.501-505, 2005.

A. Filippov, Differential equations with discontinuous right-hand side, Matematicheskii Sbornik, vol.51, pp.99-128, 1960.

A. Filippov, Differential Equations with Discontinuous Righthand Sides, Mathematics and Its Applications, 1988.

N. Fischer, R. Kamalapurkar, and W. Dixon, LaSalle-Yoshizawa corollaries for nonsmooth systems, IEEE Transactions on Automatic Control, vol.58, pp.2333-2338, 2013.

S. Flam and A. Ben-israel, A continuous approach to oligopolistic market equilibrium, vol.38, pp.1045-1051, 1990.

F. Forni, A. Tell, and L. Zaccarian, Follow the bouncing ball: Global results on tracking and state estimation with impacts, IEEE Transactions on Automatic Control, vol.58, pp.1470-1485, 2013.

M. Forti, M. Grazzini, P. Nistri, and L. Pancioni, Generalized Lyapunov approach for convergence of neural networks with discontinuous or non-Lipschitz activations, Physica D: Nonlinear Phenomena, vol.214, pp.88-99, 2006.

M. Forti, P. Nistri, and M. Quincampoix, Generalized neural network for nonsmooth nonlinear programming problems, IEEE Transactions on Circuits and Systems I: Regular Papers, vol.51, pp.1741-1754, 2004.

M. Forti, P. Nistri, and M. Quincampoix, Convergence of neural networks for programming problems via a nonsmooth Lojasiewicz inequality, IEEE Transactions on Neural Networks, vol.17, pp.1471-1486, 2006.

R. Frasca, M. Camlibel, I. Goknar, L. Iannelli, and F. Vasca, Linear passive networks with ideal switches: Consistent initial conditions and state discontinuities, IEEE Transactions on Circuits and Systems, vol.57, pp.3138-3151, 2010.

E. Fridman, L. Fridman, and E. Shustin, Steady modes in relay control systems with time delay and periodic disturbances, ASME Journal of Dynamic Systems, Measurement and Control, vol.122, pp.732-737, 2000.

T. Friesz, D. Bernstein, N. Mehta, and R. T. Ganjalizadeh, Day-to-day dynamic network disequilibria and idealized traveler information systems, Operations Research, vol.42, pp.1120-1136, 1994.

T. Friesz, M. Rigdon, and R. Mookherjee, Differential variational inequalities and shipper dynamic oligopolistic network competition, Transportation Research Part B: Methodological, vol.40, pp.480-503, 2006.

S. Gabriel, S. Kydes, and P. Whitman, The national energy modeling system: A large-scale energy-economic equilibrium model, Operations Research, vol.49, pp.14-25, 2001.

D. Gadjov and L. Pavel, A passivity-based approach to Nash equilibrium seeking over networks, IEEE Transactions on Automatic Control, vol.64, pp.1077-1092, 2018.

S. Galeani, L. Menini, and A. Tornambé, A high gain observer for the estimation of velocity and coefficient of restitution in non-smooth mechanical systems, International Journal of Modelling, Identification and Control, vol.4, pp.44-58, 2008.

K. Garg, M. Baranwal, R. Gupta, R. Vasudevan, and D. Panagou, Fixed-time stable proximal dynamical system for solving mixed variational inequality problems, 2019.

A. Gelig and G. Leonov, Monostability of multicoupled systems with discontinuous monotonic nonlinearities and non-unique equilibrium position, Automation and Remote Control, vol.6, pp.158-161, 1973.

F. Génot and B. Brogliato, New results on Painlevé paradoxes, European Journal of Mechanics A/Solids, vol.18, pp.653-678, 1999.

C. Georgescu, B. Brogliato, and V. Acary, Switching, relay and complementarity systems: a tutorial on their well-posedness and relationships, pp.1985-2002, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00646982

H. Gfrerer and J. Outrata, On computation of generalized derivatives of the normalcone mapping and their applications, Mathematics of Operations Research, vol.41, pp.1161-1207, 2016.

B. Gharesifard and J. Cortès, Distributed convergence to Nash equilibria in two-network zero-sum games, Automatica, pp.1683-1692, 2013.

P. Gidoni, Rate-independent soft crawlers, The Quarterly Journal of Mechanics and Applied Mathematics, vol.71, pp.369-409, 2018.

M. Glazos, S. Hui, and S. Zak, Sliding modes in solving convex programming problems, SIAM Journal on Control and Optimization, vol.36, pp.680-697, 1998.

C. Glocker, Impacts with global dissipation index at reentrant corners, Proc. 3rd Contact Mechanics International Symposium. Solid Mechanics and its Applications, vol.103, pp.45-52, 2001.

C. Glocker, Set-Valued Force Laws, Lecture Notes in Applied Mechanics, vol.1, 2001.

C. Glocker, An introduction to impacts, in Nonsmooth Mechanics of Solids, vol.485, 2006.

R. Goebel, Lyapunov functions and duality for convex processes, SIAM journal on Control and Optimization, vol.51, pp.3332-3350, 2013.

R. Goebel, Stability and robustness for saddle-point dynamics through monotone mappings, Systems and Control Letters, vol.108, pp.16-22, 2017.

R. Goebel and R. Sanfelice, A unifying convex analysis and switching system approach to consensus with undirected communication graphs, Automatica, p.111, 2020.

D. Goeleven, Existence and uniqueness for a linear mixed variational inequality arising in electrical circuits with transistors, Journal of Optimization Theory and Applications, vol.138, pp.397-406, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00919738

D. Goeleven, Complementarity and Variational Inequalities in Electronics, Mathematical Analysis and its Applications, 2017.

D. Goeleven, On the spider that spits the solution of a nonsmooth oscillator, Mathematical Biosciences, vol.283, pp.7-12, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01403552

D. Goeleven and B. Brogliato, Stability and instability matrices for linear evolution variational inequalities, IEEE Transactions on Automatic Control, vol.49, pp.521-534, 2004.

D. Goeleven and B. Brogliato, Necessary conditions of asymptotic stability for unilateral dynamical systems, Nonlinear Analysis: Theory, Methods and Applications, vol.61, pp.961-1004, 2005.
URL : https://hal.archives-ouvertes.fr/inria-00071417

D. Goeleven, D. Motreanu, Y. Dumont, and M. Rochdi, Variational and Hemivariational Inequalities, Theory, Methods and Applications, I: Unilateral Analysis and Unilateral Mechanics, vol.69, 2003.

D. Goeleven, D. Motreanu, and V. Motreanu, On the stability of stationary solutions of first-order evolution variational inequalities, Advances in Nonlinear Variational Inequalities, vol.6, pp.1-30, 2003.

S. Greenhalgh, V. Acary, and B. Brogliato, Preservation of the dissipativity properties of a class of nonsmooth dynamical systems with the (?, ?)-algorithm, vol.125, pp.601-637, 2013.
URL : https://hal.archives-ouvertes.fr/inria-00596961

S. Greenhalgh and M. Cojocaru, Non-equilibrium solutions of dynamic networks: a hybrid system approach, Operations Research, Engineering, and Cyber Security, vol.113, pp.299-315, 2017.

O. Güler, On the convergence of the proximal point algorithm for convex minimization, SIAM Journal on Control and Optimization, vol.29, pp.403-419, 1991.

L. Guo and J. Ye, Necessary optimality conditions for optimal control problems with equilibrium constraints, SIAM Journal on Control and Optimization, vol.54, pp.2710-2733, 2016.

L. Gurvits, R. Shorten, and O. Mason, On the stability of switched positive linear systems, IEEE Transactions on Automatic Control, vol.52, pp.1099-1103, 2007.

J. Gwinner, On differential variational inequalities and projected dynamical systemsequivalence and a stability result, Discrete and Continuous Dynamical Systems, Supplement, pp.467-476, 2007.

J. Gwinner, On a new class of differential variational inequalities and a stability result, Mathematical Programming B, vol.139, pp.205-221, 2013.

N. Ha, J. Strodiot, and P. Vuong, On the global exponential stability of a projected dynamical system for strongly pseudomonotone variational inequalities, Optimization Letters, vol.12, pp.1625-1638, 2018.

T. Ha and M. Monteiro-marques, Nonconvex second-order differential inclusions with memory, Set-Valued Analysis, vol.3, pp.71-86, 1995.

T. Haddad, Nonconvex differential variational inequality and state-dependent sweeping process, Journal of Optimization Theory and Applications, vol.159, pp.386-398, 2013.

T. Haddad and T. Haddad, Delay perturbed state-dependent sweeping process, Applicable Analysis, vol.95, pp.270-282, 2016.

T. Haddad, A. Jourani, and L. Thibault, Reduction of sweeping process to unconstrained differential inclusion, Pacific Journal of Optimization, vol.4, pp.493-512, 2008.
URL : https://hal.archives-ouvertes.fr/hal-02072909

T. Haddad, J. Noel, and L. Thibault, Perturbed sweeping process with a submooth set depending on the state, Linear and Nonlinear Analysis, vol.2, pp.155-174, 2016.

L. Han, M. Camlibel, J. Pang, and W. Heemels, A unified numerical scheme for linear-quadratic optimal control problems with joint control and state constraints, Optimization Methods and Software, vol.27, pp.761-799, 2012.

L. Han and J. Pang, Non-Zenoness of a class of differential quasi-variational inequalities, Mathematical Programming A, vol.121, pp.171-199, 2010.

L. Han, A. Tiwari, M. Camlibel, and J. Pang, Convergence of time-stepping schemes for passive and extended linear complementarity systems, SIAM Journal on Numerical Analysis, vol.47, pp.3768-3796, 2009.

A. Hantoute and M. Mazade, Lyapunov functions for evolution variational inequalities with uniformly prox-regular sets, Positivity, vol.21, pp.423-448, 2017.

A. Hantoute and E. Vilches, Lyapunov pairs for perturbed sweeping processes, Optimization Letters, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01801628

T. Hatanaka, N. Chopra, T. Ishizaki, and N. Li, passivity-based distributed optimization with communication delays using PI consensus algorithm, IEEE Transactions on Automatic Control, vol.63, pp.4421-4428, 2018.

A. Hauswirth, S. Bolognani, and F. Dorfler, Projected dynamical systems on irregular, non-euclidean domains for nonlinear optimization, 2018.

W. Heemels and B. Brogliato, The complementarity class of hybrid dynamical systems, European Journal of Control, vol.9, pp.322-360, 2003.

W. Heemels, M. Camlibel, and J. Schumacher, A time-stepping method for relay systems, Proc. IEEE 39th Conference on Decision and Control, pp.4461-4466, 2000.

W. Heemels, M. Camlibel, J. Schumacher, and B. Brogliato, Observerbased control of linear complementarity systems, Int. J. of Robust and Nonlinear Control, vol.21, pp.1193-1218, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00834580

W. Heemels, J. Schumacher, and S. Weiland, Linear complementarity systems, SIAM Journal on Applied Mathematics, vol.60, pp.1234-1269, 2000.
URL : https://hal.archives-ouvertes.fr/hal-00834580

W. Heemels, J. Schumacher, and S. Weiland, Projected dynamical systems in a complementarity formalism, Oper. Res. Lett, vol.27, pp.83-91, 2000.
URL : https://hal.archives-ouvertes.fr/hal-01660026

A. Hempel, Control of Piecewise Affine Systems Through Inverse Optimization, 2016.

C. Henry, Differential equations with discontinuous right-hand side for planning procedures, Journal of Economic Theory, vol.4, pp.545-551, 1972.

C. Henry, An existence theorem for a class of differential equations with multivalued righthand side, Journal of Mathematical Analysis and Applications, pp.179-186, 1973.

D. Henry, Geometric Theory of Semilinear Parabolic Equations, vol.840, 1981.

J. Hiriart-urruty and C. , Convex Analysis and Minimization Algorithms, vol.I, 1993.

J. Hiriart-urruty and C. , Fundamentals of Convex Analysis, Grundlehren Text Editions, 2001.

J. Hiriart-urruty and A. Seeger, A variational approach to copositive matrices, SIAM Review, vol.52, pp.593-629, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00629655

N. Hoang and B. Mordukovich, Extended Euler-Lagrange and Hamiltonian conditions in optimal control of sweeping processes with controlled moving sets, Journal of Optimization Theory and Applications, vol.180, pp.256-289, 2019.

S. Hu, Differential equations with discontinuous right-hand sides, Journal of Mathematical Analysis and Applications, vol.154, pp.377-390, 1991.

J. Huang, Y. Yang, Z. Han, and J. Zhang, Robust absolute stability criterion for uncertain Lur'e differential inclusion systems with time delay, Circuits, Systems, and Signal Processing, pp.2001-2017, 2012.

J. Huang, W. Zhang, M. Shi, L. Chen, and L. Yu, H? observer design for singular onesided lur'e differential inclusion system, Journal of the Franklin Institute, vol.354, pp.3305-3321, 2017.

O. Huber, V. Acary, and B. Brogliato, Lyapunov stability and performance analysis of the implicit discrete sliding mode control, IEEE Transactions on Automatic Control, pp.3016-3030, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01236159

L. Iannelli, R. Iervolino, and F. Vasca, Linear complementarity systems and conecopositive Lyapunov stability, IEEE Control Systems Letters, vol.3, pp.799-804, 2019.

L. Iannelli, F. Vasca, and G. Angelone, Computation of steady-state oscillations in power converters through complementarity, IEEE Transactions on Circuits and Systems-I: Regular Papers, vol.58, pp.1421-1432, 2011.

R. Iervolino, D. Tangredi, and F. Vasca, Lyapunov stability for piecewise affine systems via cone-copositivity, pp.22-29, 2017.

R. Iervolino, F. Vasca, and L. Iannelli, Cone-copositive piecewise quadratic Lyapunov functions for conewise linear systems, IEEE Transactions on Automatic Control, vol.60, pp.3077-3082, 2015.

J. Imura, Well-posedness analysis of switch-driven piecewise affine systems, IEEE Transactions on Automatic Control, vol.48, pp.1926-1935, 2003.

J. Imura, A. Van-der, and . Schaft, Characterization of well-posedness of piecewise-linear systems, IEEE Transactions on Automatic Control, vol.45, pp.1600-1619, 2002.

G. Isac and M. Cojocaru, The projection operator in a Hilbert space and its directional derivative. Consequences for the theory of projected dynamical systems, Journal of Functions Spaces and Applications, vol.2, pp.71-95, 2004.

T. Ito, A Filippov solution of a system of differential equations with discontinuous right-hand sides, Economics Letters, vol.4, pp.359-364, 1979.

A. Ivanov, Analytical methods in the theory of vibro-impact systems, J. of Applied Mathematics and Mechanics, vol.57, pp.221-236, 1993.

A. Ivanov, The stability of equilibrium in systems with friction, Journal of Applied Mathematics and Mechanics, vol.71, pp.385-395, 2007.

A. Ivanov, The equilibrium of systems with dry friction, Journal of Applied Mathematics and Mechanics, vol.79, pp.317-333, 2015.

A. Ivanov and A. Markeev, The dynamics of systems with unilateral constraints, J. of Applied Mathematics and Mechanics, vol.48, pp.448-451, 1984.

B. Jayawardhana, H. Logemann, and E. Ryan, Input-to-state stability of differential inclusions with applications to hysteretic and quantized feedback systems, SIAM Journal on Control and Optimization, vol.48, pp.1031-1054, 2009.

B. Jayawardhana, H. Logemann, and E. Ryan, The circle criterion and input-to-state stability: New perspectives on a classical result, IEEE Control Systems Magazine, pp.32-67, 2011.

B. Jayawardhana, R. Ouyang, and V. Andrieu, Stability of systems with the Duhem hysteresis operator: the dissipativity approach, pp.2657-2662, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00754365

Z. Jiang and T. Liu, Small-gain theory for stability and control of dynamical networks: a survey, Annual Reviews in Control, vol.46, pp.58-79, 2018.

A. Jokic, M. Lazar, P. Van-den, and . Bosch, On constrained steady-state regulation: dynamic KKT controllers, IEEE Transactions on Automatic Control, vol.54, pp.2250-2254, 2009.

A. Jourani and E. Vilches, Positively ?-far sets and existence results for generalized perturbed sweeping processes, Journal of Convex Analysis, vol.23, pp.775-821, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01407485

A. Jourani and E. Vilches, Galerkin-like method and generalized perturbed sweeping process with nonregular sets, SIAM Journal on Control and Optimization, vol.55, pp.2412-2436, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01611933

A. Jourani and E. Vilches, Moreau-Yosida regularization of state-dependent sweeping processes with nonregular sets, Journal of Optimization Theory and Applications, vol.173, pp.91-116, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01551688

A. Jourani and E. Vilches, A differential equation approach to implicit sweeping processes, Journal of Differential Equations, vol.266, pp.5168-5184, 2019.
URL : https://hal.archives-ouvertes.fr/hal-01961594

R. Kamath, L. Biegler, and I. Grossmann, An equation-oriented approach for handling thermodynamics based on cubic equation of state in process optimization, Computers and Chemical Engineering, vol.34, pp.2085-2096, 2010.

M. Kamenskii and O. Makarenkov, On the response of autonomous sweeping processes to periodic perturbations, Set-Valued and Variational Analysis, vol.24, pp.551-563, 2016.

M. Kamenskii, O. Makarenkov, L. Wadippuli, and P. R. De-fittec, Global stability of almost periodic solutions to monotone sweeping processes and their response to nonmonotone perturbations, Nonlinear Analysis Hybrid Systems, vol.30, pp.213-224, 2018.

C. Kanzow and D. Steck, On error bounds and multiplier methods for variational problems in Banach spaces, SIAM Journal on Control and Optimization, vol.56, pp.1716-1738, 2018.

T. Kato, Nonlinear semigroups and evolution equations, J. Math. Soc. Japan, vol.19, pp.508-520, 1967.

T. Ke, N. Loi, and V. Obukhovskii, Decay solutions for a class of fractional differential variational inequalities, Fractional Calculus and Applied Analysis, vol.16, pp.531-553, 2015.

N. Kenmochi, Solvability of nonlinear evolution equations with time-dependent constraints and applications, Bulletin of the Faculty of Education, vol.30, pp.1-87, 1981.

H. Khalil and N. Systems, , 2002.

K. Khan and P. Barton, A vector forward mode of automatic differentiation for generalized derivative evaluation, Optimization Methods and Software, vol.30, pp.1185-1212, 2015.

R. Kikuuwe and B. Brogliato, A new representation of systems with frictional unilateral constraints and its Baumgarte-like relaxation, Multibody System Dynamics, vol.39, pp.267-290, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01235861

E. Kim, J. Yang, H. Hwang, and C. Shul, Impact and blast mitigation using locally bresonant woodpile metamaterials, International Journal of Impact Engineering, vol.101, pp.24-31, 2017.

O. Klein and V. Recupero, Hausdorff metric BV discontinuity of sweeping processes, Journal of Physics: conference Series, vol.727, p.12006, 2016.

J. Kopfova and V. Recupero, BV-norm continuity of sweeping processes driven by a set with constant shape, Journal of Differential Equations, vol.261, pp.5875-5899, 2016.

S. Korovin and V. Utkin, Use of the slip mode in problems of static optimization, Automation and Remote Control, vol.33, pp.570-579, 1972.

S. Korovin and V. Utkin, Sliding mode based solution of static optimization and mathematical programming problems. applied aspects, Preprints of IFAC-IFORS Symposium, pp.1-8, 1974.

S. Korovin and V. Utkin, Using sliding modes in static optimization and nonlinear programming problems, Automatica, vol.10, pp.525-532, 1974.

S. Korovin and V. Utkin, Method of piecewise-smooth penalty functions, Automation and Remote Control, vol.37, pp.39-48, 1976.

A. and A. Pokrovskii, Dissipativity of a resonant pendulum with ferromagnetic friction, Automation and Remote Control, vol.67, pp.221-232, 2002.

P. Krejci, Evolution variational inequalities and multidimensional hysteresis operators, Nonlinear Differential Equations, vol.404, pp.47-111, 1999.

P. Krejci and V. Recupero, BV solutions of rate independent differential inclusions, Mathematica Bohemica, vol.139, pp.607-619, 2014.

P. Krejci and V. Recupero, Comparing BV solutions of rate independent processes, Journal of Convex Analysis, vol.21, pp.121-146, 2014.

P. Krejci and T. Roche, Lipschitz continuous data dependence of sweeping processes in BV spaces, Discrete and Continuous Dynamical Systems series B, vol.15, pp.637-350, 2011.

P. Krejci and A. Vladimirov, Lipschitz continuity of polyhedral Skorokhod maps, Journal for Analysis and its Applications (Zeitschrift für Analysis und ihre Anwendungen), vol.20, pp.817-844, 2001.

P. Krejci and A. Vladimirov, Polyhedral sweeping processes with oblique reflection in the space of regulated functions, Set-Valued Analysis, vol.11, pp.91-110, 2003.

K. Kuhnen and P. Krejci, Compensation of complex hysteresis and creep effects in piezoelectrically actuated systems-a new Preisach modeling approach, IEEE Transactions on Automatic Control, vol.54, pp.537-550, 2009.

M. Kunze and M. Monteiro-marques, Yosida-Moreau regularization of sweeping processes with unbounded variation, Journal of Differential Equations, vol.130, pp.292-306, 1996.

M. Kunze and M. , Monteiro-Marques, BV solutions to evolution problems with timedependent domains, Set-Valued Analysis, vol.5, pp.57-72, 1997.

M. Kunze and M. Monteiro-marques, Existence of solutions for degenerate sweeping processes, Journal of Convex Analysis, vol.4, pp.165-176, 1997.

M. Kunze and M. Monteiro-marques, On parabolic quasi-variational inequalities and state-dependent sweeping processes, Journal of the Juliusz Schauder Center, vol.12, pp.179-191, 1998.

M. Kunze and M. Monteiro-marques, On the discretization of degenerate sweeping processes, Portugaliae Mathematica, vol.55, pp.219-232, 1998.

M. Kunze and M. Monteiro-marques, An introduction to Moreau's sweeping process, Impacts in Mechanical Systems. Analysis and Modelling, B. Brogliato, vol.551, pp.1-60, 2000.

C. Landry, A. Caboussat, and E. Hairer, Solving optimization-constrained differential equations with discontinuity points, with application to atmospheric chemistry, SIAM Journal on Scientific Computing, vol.31, pp.3806-3826, 2009.

B. Le, On properties of differential inclusions with prox-regular sets, Pacific Journal of Optimization, vol.13, pp.17-27, 2017.

B. Le, Existence of solutions for sweeping processes with local conditions, Journal of Convex Analysis, p.27, 2020.

B. Le, Well-posedness and nonsmooth Lyapunov pairs for state-dependent maximal monotone differential inclusions, Optimization, 2020.

D. Leenaerts, On linear dynamic complementary systems, IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, vol.46, pp.1022-1026, 1999.

D. Leenaerts and W. Van-bokhoven, Piecewise Linear Modeling and Analysis, 1998.

D. Leeson and S. Weinreb, Frequency multiplication with nonlinear capacitors -A circuit analysis, Proceedings of the IRE, vol.47, pp.2076-2084, 1959.

R. Leine, Non-smooth stability analysis of the parametrically excited impact oscillator, International Journal of Non-Linear Mechanics, vol.47, pp.1020-1032, 2012.
URL : https://hal.archives-ouvertes.fr/hal-01403578

R. Leine, U. Aeberhard, and C. Glocker, Hamilton's principle as variational inequality for mechanical systems with impact, Journal of Nonlinear Science, vol.19, pp.633-664, 2009.
URL : https://hal.archives-ouvertes.fr/hal-01352880

R. Leine and C. Glocker, A set-valued force law for spatial Coulomb-Contensou friction, European Journal of Mechanics, vol.22, pp.193-216, 2003.

R. Leine and T. Heimsch, Global uniform symptotic attractive stability of the nonautonomous bouncing ball system, Physica D, pp.2029-2041, 2012.

R. Leine and H. Nijmeijer, Dynamics and Bifurcations of Non-Smooth Mechanical Systems, vol.18, 2004.

R. Leine and N. Van-de-wouw, Stability and Convergence of Mechanical Systems with Unilateral Constraints, vol.36, 2008.

R. Leine and N. Van-de-wouw, Uniform convergence of monotone measure differential inclusions: with application to the control of mechanical systems with unilateral constraints, International Journal of Bifurcation and Chaos, vol.15, pp.1435-1457, 2008.

G. Leonov, Stability of nonlinear controllable systems having a nonunique equilibrium position, Automation and Remote Control, vol.10, pp.23-28, 1971.

W. Li, X. Wang, and N. Huang, A system of differential set-valued variational inequalities in finite dimensional spaces, Journal of Function Spaces, vol.8, 2014.

X. Li, N. Huang, and D. O'regan, Differential mixed variational inequalities in finite dimensional spaces, Nonlinear Analysis: Theory, Methods and Applications, vol.72, pp.3875-3886, 2010.

X. Li and Z. Liu, Sensitivity analysis of optimal control problems described by differential hemivariational inequalities, SIAM Journal on Control and Optimization, vol.56, pp.3569-3597, 2018.

D. Liberzon and S. Trenn, Switched nonlinear differential algebraic equations: Solution theory, Lyapunov functions, and stability, Automatica, vol.58, pp.954-963, 2012.

M. Liberzon, Essays on the absolute stability theory, Automation and Remote Control, vol.117, pp.1610-1644, 2006.

T. Liu, Z. Jiang, and D. Hill, A sector bound approach to feedback control of nonlinear systems with state quantization, Automatica, pp.145-152, 2012.

Z. Liu, D. Motreanu, and S. Zeng, Nonlinear evolutionary systems driven by mixed variational inequalities and its applications, Nonlinear Analysis: Real World Applications, vol.42, pp.409-421, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01996806

Z. Liu, S. Zeng, and D. Motreanu, Evolutionary problems driven by variational inequalities, Journal of Differential Equations, vol.260, pp.6787-6799, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01368489

N. Loi, T. Ke, V. Obukhovskii, and P. Zecca, Topological methods for some classes of differential variational inequalities, Journal of Nonlinear and Convex Analysis, vol.17, pp.403-419, 2016.

Y. Lootsma, A. Van-der-schaft, and M. Camlibel, Uniqueness of solutions of relay systems, Automatica, vol.35, pp.467-478, 1999.

P. Lötstedt, Mechanical systems of rigid bodies subject to unilateral constraints, SIAM Journal on Applied Mathematics, vol.42, pp.281-296, 1984.

S. Lounis, T. Haddad, and M. Sene, Non-convex second-order Moreau's sweeping process in Hilbert spaces, Journal of Fixed Point Theory and Applications, vol.19, pp.2895-2908, 2017.

K. Lu, G. Jing, and L. Wang, A distributed algorithm for solving mixed equilibrium problems, Automatica, pp.246-253, 2019.

A. Lure and V. Postnikov, On the stability theory of control systems, Sov. Appl. Math, vol.8, pp.246-248, 1944.

R. Ma, X. Ban, and J. Pang, Continuous-time dynamic system optimum for singledestination traffic networks with queue spillbacks, Transportation Research Part B, vol.68, pp.98-122, 2014.

M. Mabrouk, A unified variational model for the dynamics of perfect unilateral constraints, European Journal of Mechanics A/Solids, vol.17, pp.819-842, 1998.

A. Machina and A. Ponosov, Filippov solutions in the analysis of piecewise linear models describing gene regulatory networks, Nonlinear Analysis: Theory, Methods and Applications, vol.74, pp.882-900, 2011.

A. Machina and A. Ponosov, Stability of stationary solutions of piecewise affine differential equations describing gene regulatory networks, Nonlinear Analysis: Theory, Methods and Applications, vol.380, pp.736-749, 2011.

A. Machina, A. Ponosov, and E. Voit, Automated piecewise power-law modeling of biological systems, Journal of Biotechnology, vol.149, pp.154-165, 2010.

P. Maffezzoni, L. Codecasa, and D. D'amore, Event-driven time-domain simulation of closed-loop switched circuits, IEEE Transactions on Computer-Aided design of Integrated Circuits and Systems, vol.25, pp.2413-2426, 2006.

S. Manfredi and D. Angeli, Necessary and sufficient conditions for consensus in nonlinear monotone networks with unilateral interactions, Automatica, pp.51-60, 2017.

J. Manley and H. Rowe, Some general properties of nonlinear elements -Part I. General energy relations, Proceedings of the IRE, vol.44, pp.904-913, 1956.

S. Marcellin and L. Thibault, Evolution problems associated with primal lower nice functions, Journal of Convex Analysis, vol.13, pp.385-421, 2006.

F. Martinelli, L. Menini, and A. Tornambé, Observability, reconstructibility and observer design for linear mechanical systems unobservable in absence of impacts, ASME J. Dyn. Sys., Meas., Control, pp.549-562, 2004.

B. Martinet, Régularisation d'inéquations variationnelles par approximations successives, Revue Française d'Informatique et Recherche Opérationnelle, vol.4, pp.154-158, 1970.

B. Maury and J. Venel, A discrete contact model for crowd motion, ESAIM: M2AN), vol.45, pp.145-168, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00350815

M. Mazade and L. Thibault, Differential variational inequalities with locally prox-regular sets, Journal of Convex Analysis, vol.19, pp.1109-1139, 2012.

M. Mazade and L. Thibault, Regularization of differential variational inequalities with locally prox-regular sets, Mathematical Programming B, vol.139, pp.243-269, 2013.

P. Mehlitz and G. Wachsmuth, The limiting normal cone to pointwise defined sets in Lebesgue spaces, Set-Valued and Variational Analysis, vol.26, pp.449-467, 2018.

L. Menini and A. Tornambé, Asymptotic tracking of periodic trajectories for a simple mechanical system subject to nonsmooth impacts, IEEE Transactions on Automatic Control, vol.46, pp.1122-1126, 2001.

L. Menini and A. Tornambé, State estimation of (otherwise unobservable) linear mechanical systems through the use of non-smooth impacts: the case of two mating gears, vol.38, pp.1823-1826, 2002.

L. Menini and A. Tornambé, Velocity observers for non-linear mechanical systems subject to non-smooth impacts, Automatica, vol.38, pp.2169-2175, 2002.

S. Migorski and S. Zeng, A class of generalized evolutionary problems driven by variational inequalities and fractional operators, Set-Valued and Variational Analysis, vol.27, pp.949-970, 2019.

F. Miranda-villatoro, B. Brogliato, and F. Castanos, Multivalued robust tracking control of Lagrange systems: Continuous and discrete-time algorithms, IEEE Transactions on Automatic Control, vol.62, pp.4436-4450, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01254303

F. Miranda-villatoro, B. Brogliato, and F. Castanos, Set-valued sliding mode control of uncertain linear systems: Continuous and discrete-time analysis, SIAM Journal on Control and Optimization, vol.56, pp.1756-1793, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01317948

F. Miranda-villatoro and F. Castanos, Robust output regulation of strongly passive linear systems with multivalued maximally monotone controls, IEEE Transactions on Automatic Control, vol.62, pp.238-249, 2017.

F. Miranda-villatoro, F. Castanos, and B. Brogliato, Continuous and discrete-time stability of a robust set-valued nested controller, Automatica, vol.107, pp.406-417, 2019.
URL : https://hal.archives-ouvertes.fr/hal-01944920

M. Monteiro-marques, Perturbations convexes semi-continues supérieurement de problèmes d'évolution dans les espaces de Hilbert, Travaux du Séminaire d'Analyse Convexe de, 1984.

M. Monteiro-marques, Chocs inélastiques standards: un résultat d'existence, vol.4, 1985.

M. Monteiro-marques, Differential Inclusions in Nonsmooth Mechanical Problems. Shocks and Dry Friction, vol.9, 1993.

C. Morarescu and B. Brogliato, Passivity-based switching control of flexible-joint complementarity mechanical systems, Automatica, vol.46, pp.160-166, 2010.
URL : https://hal.archives-ouvertes.fr/inria-00342292

C. Morarescu and B. Brogliato, Trajectory tracking control of multiconstraint complementarity lagrangian systems, IEEE Transactions on Automatic Control, vol.55, pp.1300-1313, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00756307

B. Mordukhovich, Variational Analysis and Generalized Differentiation I: Basic Theory, Comprehensive Studies in Mathematics, vol.330, 2006.

B. Mordukhovich, Variational Analysis and Applications, Springer Monographs in Mathematics, 2018.

J. Moreau, Les liaisons unilatérales et le principe de Gauss, vol.256, pp.871-874, 1963.

J. Moreau, Quadratic programming in mechanics: dynamics of one sided constraints, J. SIAM Control series A, vol.4, pp.153-158, 1966.
URL : https://hal.archives-ouvertes.fr/hal-01379713

J. Moreau, Rafle par un convexe variable I. Sém. Anal. Convexe Montpellier, France, exposé 15, 1971.

J. Moreau, Rafle par un convexe mobile dans un espace hilbertien, Colloque d'Analyse Non-linéaire, 1972.
URL : https://hal.archives-ouvertes.fr/hal-01795265

J. Moreau, Rafle par un convexe variable II, Sém. Anal. Convexe Montpellier, vol.3, 1972.

J. Moreau, On unilateral constraints, friction and plasticity, New Variational Techniques in Mathematical Physics, pp.173-222, 1974.
URL : https://hal.archives-ouvertes.fr/hal-01793413

J. Moreau, Application of convex analysis to the treatment of elastoplastic systems, Applications of Methods of Functional Analysis to Problems of Mechanics, Joint Symposium IUTAM/IMU, pp.56-89, 1976.

J. Moreau, Preliminary version in: Problème d'évolution associéà un convexe mobile d'un espace Hilbertien. Comptes Rendus de l, Journal of Differential Equations, vol.26, pp.791-794, 1973.

J. Moreau, Application of convex analysis to some problems of dry friction, Trends in Applications of Pure Mathematics to Mechanics, H. Zorski, vol.2, pp.263-280, 1979.
URL : https://hal.archives-ouvertes.fr/hal-01864012

J. Moreau, Liaisons unilatérales sans frottement et chocs inélastiques, C.R. Acad. Sci. Paris, pp.1473-1476, 1983.

J. Moreau, Unilateral contact and dry friction in finite freedom dynamics, in Nonsmooth Mechanics and Applications, CISM Courses and Lectures, vol.302, pp.1-82, 1988.

J. Moreau, Numerical aspects of the sweeping process, Computer Methods in Applied Mechanics and Engineering, vol.177, pp.329-349, 1999.
URL : https://hal.archives-ouvertes.fr/hal-01349847

F. Nacry, Preturbed BV sweeping process involving prox-regular sets, Journal of Nonlinear and Convex Analysis, vol.18, pp.1619-1651, 2017.

F. Nacry, Truncated nonconvex state-dependent sweeping process: implicit and semi-implicit adapted Moreau's catching-up algorithms, Journal of Fixed Point Theory and Applications, vol.20, p.121, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01862612

F. Nacry and L. Thibault, BV prox-regular sweeping process with bounded truncated variation, Optimization, 2018.

A. Nagurney, J. Cruz, and D. Matsypura, Dynamics of global supply chain supernetworks, Mathematical and Computer Modelling, vol.37, pp.963-983, 2003.

A. Nagurney and J. Pan, Evolution variational inequalities and projected dynamical systems with application to human migration, Mathematical and Computer Modelling, vol.43, pp.646-657, 2006.

A. Nagurney and D. Zhang, Projected Dynamical Systems and variational Inequalities, 1995.

J. Noel, Second order general perturbed sweeping process differential inclusion, Journal of Fixed Point Theory and Applications, vol.20, p.133, 2018.

M. Oguztöreli, Relay type control systems with retardation and switching delay, J. SIAM Control series A, vol.1, pp.275-289, 1963.

Y. Or and A. Ames, Stability and completion of Zeno equilibria in lagrangian hybrid systems, IEEE Transactions on Automatic Control, vol.56, pp.1322-1336, 2011.

Y. Or and A. Teel, Zeno stability of the set-valued bouncing ball, IEEE Transactions on Automatic Control, vol.56, pp.447-452, 2011.

Y. Orlov, Finite time stability and robust control synthesis of uncertain switched systems, SIAM Journal on Control and Optimization, vol.43, pp.1253-1271, 2005.

Y. Orlov and D. Systems, Lyapunov Analysis and Robust Synthesis under Uncertainty Conditions, 2009.

M. Otani, On existence of strong solutions for du dt (t) + ?? 1 (u(t)) ? ?? 2 (u(t)) f (t), Journal of the Faculty of Science, the University of Tokyo. Sect. 1 A, Mathematics, vol.24, pp.575-605, 1977.

R. Ouyang and B. Jayawardhana, Absolute stability analysis of linear systems with Duhem hysteresis operator, Automatica, vol.50, pp.1860-1866, 2014.

H. Oza, Y. Orlov, and S. Spurgeon, Finite time stabilization of a perturbed double integrator with unilateral constraints, Mathematics and Computers in Simulation, vol.95, pp.200-212, 2013.

H. Oza, Y. Orlov, and S. Spurgeon, A unified Lyapunov function for finite time stabilization of continuous and variable structure systems with resets, Proc. IEEE 55th Conference on Decision and Control, pp.2201-2206, 2016.

J. Pang, L. Han, G. Ramadurai, and S. Ukkusuri, A continuous-time linear complementarity system for dynamic user equilibria in single bottleneck traffic flows, Mathematical Programming A, vol.133, pp.437-460, 2012.

J. Pang and J. Shen, Strongly regular differential variational systems, IEEE Transactions on Automatic Control, vol.52, pp.242-255, 2007.

J. Pang and D. Stewart, Differential variational inequalities, Mathematical Programming A, vol.113, pp.345-424, 2008.

J. Pang and D. Stewart, Solution dependence on initial conditions in differential variational inequalities, Mathematical Programming B, vol.116, pp.429-460, 2009.

L. Paoli, Continuous dependence on data for vibro-impact problems, Math. Models Methods Appl. Sci. (M3AS), vol.35, pp.1-41, 2005.

L. Paoli, Vibro-impact problems with dry friction-part I: Existence result, SIAM Journal on Mathematical Analysis, vol.47, pp.3285-3313, 2015.
URL : https://hal.archives-ouvertes.fr/hal-02074443

L. Paoli, Vibro-impact problems with dry friction-part II: Tangential contacts and frictional catastrophes, SIAM Journal on Mathematical Analysis, vol.48, pp.1272-1296, 2016.
URL : https://hal.archives-ouvertes.fr/hal-02074455

L. Paoli and M. Schatzman, Mouvementà un nombre fini de degrés de liberté avec contraintes unilatérales : cas avec perte d'énergie, RAIRO-Modélisation mathématique et analyse numérique, vol.27, pp.673-717, 1993.

M. Pappalardo and M. Passacantando, Stability for equilibrium problems: from variational inequalities to dynamical systems, Journal of Optimization Theory and Applications, vol.113, pp.567-582, 2002.

T. Paré, A. Hassibi, and J. How, A KYP lemma and invariance principle for systems with multiple hysteresis non-linearities, International Journal of Control, vol.74, pp.1140-1157, 2001.

N. Pavel, Nonlinear Evolution Operators and Semigroups: Applications to Partial Differential Equations, vol.1260, 1987.

P. Pécol, P. Argoul, S. D. Pont, and S. Erlicher, The non-smooth view for contact dynamics by Michel Frémond extended to the modelling of crowd movements, Discrete and Continuous Dynamical Systems Series S, vol.6, pp.547-565, 2013.

P. Pécol, S. D. Pont, S. Erlicher, and P. Argoul, Smooth/non-smooth contact modeling of human crowds movement: numerical aspects and application to emergency evacuations, Ann. Solid Struct. Mech, vol.2, pp.69-85, 2011.

D. Percivale, Uniqueness in the elastic bounce problem, Journal of Differential Equations, vol.56, pp.206-215, 1985.
URL : https://hal.archives-ouvertes.fr/hal-01544491

D. Percivale, Uniqueness in the elastic bounce problem, Journal of Differential Equations, vol.II, pp.304-315, 1991.
URL : https://hal.archives-ouvertes.fr/hal-01544491

C. D. Persis and S. Grammatico, Continuous-time integral dynamics for monotone aggregative games with coupling constraints, IEEE Transactions on Automatic Control, 2019.

C. D. Persis and S. Grammatico, Distributed averaging integral Nash equilibrium seeking on networks, Automatica, p.110, 2019.

J. Peypouquet and S. Sorin, Evolution equations for maximal monotone operators: asymptotic analysis in continuous and discrete time, Journal of Convex Analysis, vol.17, pp.1113-1163, 2010.

F. Pfeiffer and C. Glocker, Multibody Dynamics with Unilateral Contacts, Nonlinear Science, 1996.

L. Pipes, Analysis of electric circuits containing noninear resistance, Journal of the Franklin Institute, vol.263, pp.47-55, 1957.

A. Pogromsky, W. Heemels, and H. Nijmeijer, On solution concepts and well-posedness of linear relay systems, Automatica, pp.2139-2147, 2003.

A. Polyakov, D. Efimov, and B. Brogliato, Consistent discretization of finite-time and fixed-time stable systems, SIAM Journal on Control and Optimization, vol.57, pp.78-103, 2019.
URL : https://hal.archives-ouvertes.fr/hal-01838712

E. Pratt, A. Léger, and M. Jean, About a stability conjecture concerning unilateral contact with friction, Nonlinear Dynamics, vol.59, pp.73-94, 2010.
URL : https://hal.archives-ouvertes.fr/hal-01580814

A. Raghunathan, J. Perez-correa, E. Agosin, and L. Biegler, Parameter estimation in metabolic flux balance models for batch fermentation-formulation and solution using differential variational inequalities, Oper. Res, vol.148, pp.251-270, 2006.

A. Raghunathan, M. Soledad-diaz, and L. Biegler, An MPEC formulation for dynamic optimization of distillation operations, Computers and Chemical Engineering, vol.28, pp.2037-2052, 2009.

V. Recupero, A continuity method for sweeping process, Journal of Differential Equations, pp.2125-2142, 2011.

V. Recupero, BV continuous sweeping processes, Journal of Differential Equations, vol.259, pp.4253-4272, 2015.

V. Recupero, Convex valued geodesics and applications to sweeping processes with bounded retraction, Journal of Convex Analysis, p.27, 2020.

V. Recupero and F. Santambrogio, Sweeping processes with prescribed behaviour on jumps, Annali di Matematica, vol.197, pp.1311-1332, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01570514

S. Robinson, Generalized equations and their solutions. I Basic theory, Mathematical Programming Study, vol.10, pp.128-141, 1979.

R. Rockafellar, Monotone Processes of Convex and Concave Type, vol.77, 1967.

R. Rockafellar, Convex Analysis, 1970.

R. Rockafellar and R. Wets, Comprehensive Studies in Mathematics, vol.317, 1998.

A. Rodriguez-vasquez, R. Dominguez-castro, A. Rueda, J. Huertas, and E. Sanchez-sinencio, Nonlinear switched-capacitor "neural" networks for optimization problems, IEEE Transactions on Circuits and Systems, vol.37, pp.384-398, 1990.

N. Rouche and J. Mawhin, Equations Différentielles Ordinaires, vol.2, 1973.

E. Ryan, An integral invariance principle for differential inclusions with applications in adaptive control, SIAM Journal on Control and Optimization, vol.36, pp.960-980, 1998.

A. Sahlodin, H. Watson, and P. Barton, Nonsmooth model for dynamic simulation of phase changes, AIChE Journal, vol.62, pp.3334-3351, 2016.

D. Salas, L. Thibault, and E. Vilches, On smoothness of solutions to projected differential equations, Discrete and Continuous Dynamical Systems, vol.39, pp.2255-2283, 2019.

M. Schatzman, A class of nonlinear differential equations of second order in time, Nonlinear Analysis: Theory, Methods and Applications, vol.2, pp.355-373, 1978.
URL : https://hal.archives-ouvertes.fr/hal-01294058

M. Schatzman, Uniqueness and continuous dependence on data for one-dimensional impact problems, Mathematical and Computer Modelling, vol.28, pp.1-18, 1998.
URL : https://hal.archives-ouvertes.fr/hal-01544389

C. Scherer and T. Holicki, An IQC theorem for relations: towards stability analysis of data-integrated systems, 9th IFAC Symposium on Robust Control Design, Florianopolis, 2018.

M. Schulz and S. Pellegrino, Equilibrium paths of mechanical systems with unilateral constraints I. Theory, Proceedings Royal Soc. London A: Mathematical, Physical and Engineeriong Sciences, vol.456, pp.2223-2242, 2000.
URL : https://hal.archives-ouvertes.fr/hal-01395595

J. Schumacher, Complementarity systems in optimization, Mathematical Programming B, vol.101, pp.263-295, 2004.

L. Schwartz, Théorie des Distributions, 1966.

M. Sene and L. Thibault, Regularization of dynamical systems associated with prox-regular moving sets, Journal of Nonlinear and Convex Analysis, vol.15, pp.647-663, 2014.
URL : https://hal.archives-ouvertes.fr/hal-02073061

O. Serea, On reflecting boundary problem for optimal control problem, SIAM Journal on Control and Optimization, vol.42, pp.559-575, 2003.
URL : https://hal.archives-ouvertes.fr/hal-01660024

O. Serea, Optimality conditions for reflecting boundary control problems, Nonlinear Differential Equations and Applications NoDEA, vol.20, pp.1225-1242, 2013.

V. Sessa, L. Iannelli, and F. Vasca, A complementarity model for closed-loop power converters, IEEE Transactions on Power Electronics, vol.29, pp.6821-6835, 2014.

V. Sessa, L. Iannelli, F. Vasca, and V. Acary, A complementarity approach for the computation of periodic oscillations in piecewise linear systems, Nonlinear Dynamics, vol.85, pp.1255-1273, 2016.

J. Shen and J. Pang, Linear complementarity systems: Zeno states, SIAM Journal on Control and Optimization, vol.44, pp.1040-1066, 2005.

J. Shen and J. Pang, Semicopositive linear complementarity systems, Int. Journal of Robust and Nonlinear Control, vol.17, pp.1367-1386, 2007.

M. Shi, J. Huang, L. Chen, and L. Yu, Adaptive full-order and reduced-order observers for one-sided Lur'e systems with set-valued mappings, IMA Journal of Mathematical Control and Information, vol.35, pp.569-589, 2016.

A. Siddiqi, P. Manchanda, and M. Brokate, On some recent developments concerning Moreau's sweeping process, Proceedings of the 1st International Conference on Industrial and Applied Mathematics of the Indian Subcontinent: Trends in Industrial and Applied Mathematics, pp.339-354, 2002.

G. Smirnov, Introduction to the Theory of Differential Inclusions, vol.41, 2002.

J. Sponsel, S. Bundfuss, and M. Dür, An improved algorithm to test copositivity, Journal of Global Optimization, vol.52, pp.537-551, 2012.

J. Spraker and D. Biles, A comparison of the Carathéodory and Filippov solution sets, Journal of Mathematical Analysis and Applications, vol.198, pp.571-580, 1996.

P. Stechlinski, M. Patrascu, and P. Barton, Nonsmooth differential-algebraic equations in chemical engineering, Computers and Chemical Engineering, vol.114, pp.52-68, 2018.

T. Stegink, T. Van-damme, and C. De-persis, Convergence of projected primal-dual dynamics with applications in data centers, 7th IFAC Workshop on Distributed Estimation and Control in Networked Systems NECSYS, vol.51, pp.88-93, 2018.

D. Stewart, A high accuracy method for solving ODEs with discontinuity right-hand side, Numerische Mathematik, pp.299-328, 1990.

D. Stewart, Convergence of a time-stepping scheme for rigid-body dynamics and resolution of Painlevé's problem, Archive for Rational Mechanics and Analysis, vol.145, pp.215-260, 1998.

D. Stewart, Uniqueness for index-one differential variational inequalities, Nonlinear Analysis: Hybrid Systems, vol.2, pp.812-818, 2008.

D. Stewart and J. Trinkle, An implicit time-stepping scheme rigid body dynamics with inelastic collisions and Coulomb friction, Int. J. Numer. Methods Eng, vol.39, pp.2673-2691, 1996.

A. Tanwani, B. Brogliato, and C. Prieur, Stability and observer design for Lur'e systems with multivalued, non-monotone, time-varying nonlinearities and state jumps, SIAM Journal on Control and Optimization, vol.56, pp.3639-3672, 2014.

A. Tanwani, B. Brogliato, and C. Prieur, Observer design for unilaterally constrained Lagrangian systems: A passivity-based approach, IEEE Transactions on Automatic Control, pp.2386-2401, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01113344

A. Tanwani, B. Brogliato, and C. Prieur, Well-posedness and output regulation for implicit time-varying evolution variational inequalities, SIAM Journal on Control and Optimization, vol.56, pp.751-781, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01360325

A. Tanwani and S. Trenn, Determinability and state estimation for switched differentialalgebraic equations, Automatica, pp.17-31, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01462885

A. Tanwani and Q. Zhu, Feedback Nash equilibrium for randomly switching differentialalgebraic games, IEEE Transactions on Automatic Control, 2020.

A. Tasora, M. Anitescu, S. Negrini, and D. Negrut, A compliant visco-plastic particle contact model based on differential variational inequalities, International Journal of Non-Linear Mechanics, vol.53, pp.2-12, 2013.

A. Dam, K. Dwarshuis, and J. Willems, The contact problem for linear continuous-time dynamical systems: a geometric approach, IEEE Transactions on Automatic Control, vol.42, pp.458-472, 1997.

L. Thibault, Propriétés des sous-différentiels de fonctions localement lipschitziennes definies sur un espace de Banach séparable, Applications, 1975.

L. Thibault, Sweeping process with regular and nonregular sets, Journal of Differential Equations, vol.193, pp.1-26, 2003.

L. Thibault, Moreau sweeping process with bounded truncated retraction, Journal of Convex Analysis, vol.23, pp.1051-1098, 2016.
URL : https://hal.archives-ouvertes.fr/hal-02072790

L. Thuan and M. Camlibel, Continuous piecewise affine dynamical systems do not exhibit Zeno behavior, IEEE Transactions on Automatic Control, vol.56, pp.1932-1936, 2011.

L. Thuan and M. Camlibel, Controllability and stabilizability of a class of continuous piecewise affine dynamical systems, SIAM Journal on Control and Optimization, vol.52, pp.1914-1934, 2014.

L. Thuan and M. Camlibel, On the existence, uniqueness and nature of Carathéodory and Filippov solutions for bimodal piecewise affine dynamical systems, Systems and Control Letters, vol.68, pp.76-85, 2014.

A. Tolstogonov, Sweeping process with unbounded nonconvex perturbation, Nonlinear Analysis, vol.108, pp.291-301, 2014.

A. Tolstogonov, Control sweeping processes, Journal of Convex Analysis, vol.23, pp.1099-1123, 2016.

A. Tolstogonov, Relaxation in nonconvex optimal control problems containing the difference of two subdifferentials, SIAM Journal on Control and Optimization, vol.54, pp.175-197, 2016.

A. Tolstogonov, Existence and relaxation of solutions for a subdifferential inclusion with unbounded perturbation, Journal of Mathematical Analysis and Applications, vol.447, pp.269-288, 2017.

A. Tolstogonov, Polyhedral sweeping processes with unbounded nonconvex-valued perturbation, Journal of Differential Equations, vol.263, pp.7965-7983, 2017.

A. Tolstogonov, Filippov-Wazewski theorem for subdifferential inclusions with an unbounded perturbation, SIAM Journal on Control and Optimization, vol.56, pp.2878-2900, 2018.

N. Tschoegl, The Phenomenological Theory of Linear Viscoelastic Behaviour. An Introduction, 1989.

V. Utkin, Sliding Modes in Control and Optimization, Communications and Control Engineering, 1992.

M. Valadier, Quelques problèmes d'entrainement unilatéral en dimension finie, Séminaire d'Analyse Convexe, vol.8, 1988.

M. Valadier, Lipschitz approximation of the sweeping (or Moreau) process, Journal of Differentila Equations, vol.88, pp.248-264, 1990.

M. Valadier, Rafle et viabilité, Séminaire d'Analyse Convexe, vol.17, 1992.

W. Van-bokhoven and D. Leenaerts, Explicit formulas for the solutions of piecewise linear networks, IEEE Transactions on Circuits and Systems. I, Fundamental Theory and Applications, vol.46, pp.1110-1117, 1999.

N. Van-de-wouw and R. Leine, Attractivity of equilibrium sets of systems with dry friction, Nonlinear Dynamics, vol.35, pp.19-39, 2004.

A. Van-der-schaft and J. Schumacher, The complementary-slackness class of hybrid systems, Mathematics of Control, Signals and Systems, vol.9, pp.266-301, 1996.

A. Van-der-schaft and J. Schumacher, Complementarity modeling of hybrid systems, IEEE Transactions on Automatic Control, vol.43, pp.483-490, 1998.

N. Van-loi, M. Vu, and P. Cuong, Nonlocal problem for differential complementarity systems, Applied Mathematics and Computation, vol.265, pp.799-806, 2015.

L. Vandenberghe, B. De-moor, and J. Vandewalle, The generalized linear complementarity problem applied to the complete analysis of resistive piecewise-linear circuits, IEEE Transactions on Circuits and Systems, vol.36, pp.1382-1391, 1989.

F. Vasca, L. Iannelli, M. Camlibel, and R. Frasca, A new perspective for modeling power electronics converters: complementarity framework, IEEE Transactions on Power Electronics, vol.24, pp.456-468, 2009.

M. Vidyasagar, Nonlinear Systems Analysis, 1993.

A. Vieira, B. Brogliato, and C. Prieur, Optimality conditions for the minimal time problem for complementarity systems, Proceedings of 11th IFAC Nonlinear Control Systems NOLCOS, pp.325-330, 2019.
URL : https://hal.archives-ouvertes.fr/hal-01856054

A. Vieira, B. Brogliato, and C. Prieur, Quadratic optimal control of linear complementarity systems: first order necessary conditions and numerical analysis, IEEE Transactions on Automatic Control, 2020.
URL : https://hal.archives-ouvertes.fr/hal-01690400

E. Vilches, Existence and Lyapunov pairs for the perturbed sweeping process governed by a fixed set, Set-Valued Var. Anal, vol.27, pp.569-583, 2019.
URL : https://hal.archives-ouvertes.fr/hal-02194585

A. Visintin, Differential Models of Hysteresis, vol.111, 1994.

A. Visintin, Mathematical models of hysteresis, The Science of Hysteresis, vol.1, pp.1-123, 2005.

A. Vladimirov, Equicontinuous sweeping processes, Discrete and Continuous Dynamical Systems B, vol.18, pp.565-573, 2013.

A. Vladimirov, Nonstationary dissipative evolution equations in a Hilbert space, Nonlinear Analysis, vol.17, pp.499-518, 1991.

T. Vromen, N. Van-de-wouw, A. Doris, P. Astrid, and H. Nijmeijer, Nonlinear outputfeedback control of torsional vibrations in drilling systems, Int. Journal of Robust and Nonlinear Control, vol.27, pp.3659-3684, 2017.

L. Wadippuli, I. Gudoshnikov, and O. Makarenkov, Global asymptotic stability of nonconvex sweeping processes, Discrete and Continuous Dynamical Systems Series B, 2020.

D. Wang and B. Du, Continuum modelling of spatial and dynamic equilibrium in a travel corridor with hererogeneous commuters-a partial differential complementarity system approach, Transportation Research Part B, vol.85, pp.1-18, 2016.

X. Wang and N. Huang, Differential vector variational inequalities in finite-dimensional spaces, Journal of Optimization Theory and Applications, vol.158, pp.109-129, 2013.

X. Wang and N. Huang, A class of differential vector variational inequalities in finite dimensional spaces, Journal of Optimization Theory and Applications, vol.162, pp.633-648, 2014.

X. Wang, Y. Qi, C. Tao, and Y. Xiao, A class of delay differential variational inequalities, Journal of Optimization Theory and Applications, vol.172, pp.56-69, 2017.

Y. Wang, Dynamic modeling and stability analysis of mechanical systems with time-varying topologies, ASME Journal of Mechanical Design, vol.115, pp.808-816, 1993.
URL : https://hal.archives-ouvertes.fr/hal-01970469

Y. Wang, Global analysis and simulation of mechanical systems with time-varying topologies, ASME Journal of Mechanical Design, vol.115, pp.817-821, 1993.

C. Wu, K. Teo, V. Rehbock, and G. Liu, Existence and uniqueness of solutions of piecewise nonlinear systems, Nonlinear Analysis Theory Methods and Applications, vol.12, pp.6109-6115, 2009.

Y. Xia, H. Leung, and J. Wang, A projection neural network and its application to constrained optimization problems, IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications, vol.49, pp.447-458, 2002.

Y. Xia and J. Wang, On the stability of globally projected dynamical systems, Journal of Optimization Theory and Applications, vol.106, pp.129-150, 2000.

V. Yakubovich, The method of matrix inequalities in the stability theory of nonlinear control systems III. absolute stability of systems with hysteresis nonlinearities, Automation and Remote Control, vol.26, pp.753-763, 1967.

V. Yakubovich, The conditions for absolute stability of a control system with a hysteresistype nonlinearity, Soviet. Phys. Dokl, vol.8, pp.235-237, 1963.

V. Yakubovich, Frequency conditions for the absolute stability of control systems with several nonlinear or linear nonstationary blocks, Avtomat. i Telemekh, vol.6, pp.5-30, 1967.

V. Yakubovich, G. Leonov, and A. Gelig, of Stability, Vibration and Control Systems, Stability of Stationary Sets in Control Systems with Discontinuous Nonlinearities, vol.14, 2004.

Z. Yazdaniyan, M. Shamsi, Z. Foroozandeh, and M. De-pinho, A numerical method based on the complementarity and optimal control formulations for solving a family of zero-sum pursuit-evasion differential games, Journal of Computational and Applied Mathematics, 2020.

Z. Ye, Q. Wang, C. Lin, C. Hang, and A. Barabanov, Relay feedback analysis for a class of servo plants, Journal of Mathematical Analysis and Applications, vol.334, pp.28-42, 2007.

P. Yi, Y. Hong, and F. Liu, Initialization-free distrubuted algorithms for optimal resource allocation with feasibility constraints and application to economic dispatch of power systems, Automatica, vol.74, pp.259-269, 2016.

K. Yoshida, M. Inoue, and T. Hatanaka, Instant MPC for linear systems and dissipativitybased stability analysis, IEEE Control Systems Letters, 2019.

Y. Yuan, M. Li, J. Liu, and C. Tomlin, On the powerball method: variants of descent methods for accelerated optimization, IEEE Control Systems Letters, vol.3, pp.601-606, 2019.

G. Zames, On the input-output stability of nonlinear time-varying feedback systems-part I, IEEE Transactions on Automatic Control, vol.11, pp.228-238, 1966.

G. Zames, On the input-output stability of nonlinear time-varying feedback systems-part II, IEEE Transactions on Automatic Control, vol.11, pp.465-477, 1966.

X. Zeng, J. Chen, S. Liang, and Y. Hong, Generalized Nash equilibrium seeking strategy for distributed nonsmooth multi-cluster game, Automatica, vol.103, pp.20-26, 2019.

D. Zhang and A. Nagurney, On the stability of projected dynamical systems, Journal of Optimization Theory and Applications, vol.85, pp.97-124, 1995.

H. Zhang, J. Wei, P. Yi, and X. Hu, Projected primal-dual gradient flow of augmented Lagrangian with application to distributed maximization of the algebraic connectivity of a network, Automatica, vol.98, pp.34-41, 2018.

T. Zhao, Z. Li, and Z. Ding, Consensus-based distributed optimal energy management with less communication in a microgrid, IEEE Transactions on Industrial Informatics, vol.15, pp.3356-3367, 2019.

R. Zhong, F. Yuan, and T. Pan, A linear complementarity system approach to macroscopic freeway traffic modeling, Proc. IEEE Int. Conference on Cyber Technology in Automation, Control and Intelligent Systems, pp.18-23, 2013.

R. Zhong, A. Sumalee, T. Friesz, and W. Lam, Dynamic user equilibrium with side constraints for a traffic network: Theoretical development and numerical solution algorithm, Transportation Research Part B: Methodological, vol.45, pp.1035-1061, 2011.

R. Zhong, F. Yuan, T. Pan, A. Chow, C. Chen et al., Linear complementarity system approach to macroscopic freeway traffic modelling: uniqueness and convexity, vol.12, pp.142-174, 2016.

V. Zhuravlev, A method for analysing vibration-impact systems by means of special functions, Mekhanika Tverdogo Tela (Mechanics of Solids), vol.11, pp.23-27, 1976.

T. Zolezzi, Differential inclusions and sliding mode control, in Sliding Mode Control in Engineering, pp.29-52, 2002.