V. Acary and B. Brogliato, Implicit Euler numerical scheme and chattering-free implementation of sliding mode systems, Systems & Control Letters, vol.59, issue.5, pp.284-293, 2010.
DOI : 10.1016/j.sysconle.2010.03.002
URL : https://hal.archives-ouvertes.fr/inria-00423576

V. Acary, B. Brogliato, and Y. V. Orlov, Chattering-free digital sliding-mode control with state observer and disturbance rejection. Automatic Control, IEEE Transactions on, vol.57, issue.5, pp.1087-1101, 2012.
URL : https://hal.archives-ouvertes.fr/inria-00580713

S. Adly, H. Attouch, and A. Cabot, Finite Time Stabilization of Nonlinear Oscillators Subject to dry Friction, Progresses in Nonsmooth Mechanics and Analysis, chapter 24
DOI : 10.1007/0-387-29195-4_24
URL : https://hal.archives-ouvertes.fr/hal-00068295

J. Aubin and A. Cellina, Differential Inclusions: Set-Valued Maps and Viability Theory. Grundlehren der mathematischen Wissenschaften, 1984.

B. Baji and A. Cabot, An inertial proximal algorithm with dry friction: finite convergence results. Set-Valued Analysis, pp.1-23, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00068884

J. Bastien, Convergence order of implicit Euler numerical scheme for maximal monotone differential inclusions, Zeitschrift für angewandte Mathematik und Physik, pp.955-966, 2013.
DOI : 10.1007/s00033-012-0276-y

H. Bauschke and P. Combettes, Convex Analysis and Monotone Operator Theory in Hilbert Spaces, CMS Books in Mathematics, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00643354

S. Boyd, L. Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, Studies in Applied Mathematics. Society for Industrial and Applied Mathematics, 1994.
DOI : 10.1137/1.9781611970777

H. Brézis, Opérateurs Maximaux Monotones et Semi-groupes de Contractions dans les Espaces de Hilbert. Number 5 in North-Holland mathematics studies, 1973.

B. Brogliato and D. Goeleven, Well-posedness, stability and invariance results for a class of multivalued Lur???e dynamical systems, Nonlinear Analysis: Theory, Methods & Applications, vol.74, issue.1, pp.195-212, 2011.
DOI : 10.1016/j.na.2010.08.034
URL : https://hal.archives-ouvertes.fr/hal-00845341

B. Brogliato, A. Daniilidis, C. Lemaréchal, and V. Acary, On the equivalence between complementarity systems, projected systems and differential inclusions, Systems & Control Letters, vol.55, issue.1, pp.45-51, 2006.
DOI : 10.1016/j.sysconle.2005.04.015
URL : https://hal.archives-ouvertes.fr/inria-00071475

M. Camlibel and J. Schumacher, Linear passive systems and maximal monotone mappings, Mathematical Programming, pp.1-24, 2015.
DOI : 10.1007/s10107-015-0945-7

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

F. Castaños and L. Fridman, Analysis and design of integral sliding manifolds for systems with unmatched perturbations. Automatic Control, IEEE Transactions on, vol.51, issue.5, pp.853-858, 2006.

A. Cellina and M. Marchi, Non-convex perturbations of maximal monotone differential inclusions, Israel Journal of Mathematics, vol.12, issue.1-2, pp.1-11, 1983.
DOI : 10.1007/BF02760619

H. H. Choi, A new method for variable structure control system design: A linear matrix inequality approach, Automatica, vol.33, issue.11, pp.2089-2092, 1997.
DOI : 10.1016/S0005-1098(97)00118-0

H. H. Choi, An LMI-based switching surface design method for a class of mismatched uncertain systems, IEEE Transactions on Automatic Control, vol.48, issue.9, pp.1634-1638, 2003.
DOI : 10.1109/TAC.2003.817007

J. Cortés, Discontinuous dynamical systems, IEEE Control Systems Magazine, vol.28, issue.3, pp.36-73, 2008.
DOI : 10.1109/MCS.2008.919306

J. F. Edmond and L. Thibault, BV solutions of nonconvex sweeping process differential inclusion with perturbation, Journal of Differential Equations, vol.226, issue.1, pp.135-179, 2006.
DOI : 10.1016/j.jde.2005.12.005

A. Filippov and F. Arscott, Differential Equations with Discontinuous Righthand Sides: Control Systems. Mathematics and its Applications, 1988.
DOI : 10.1007/978-94-015-7793-9

Z. Galias and X. Yu, Euler's Discretization of Single Input Sliding-Mode Control Systems, IEEE Transactions on Automatic Control, vol.52, issue.9, pp.1726-1730, 2007.
DOI : 10.1109/TAC.2007.904289

Z. Galias and X. Yu, Analysis of Zero-Order Holder Discretization of Two-Dimensional Sliding-Mode Control Systems, IEEE Transactions on Circuits and Systems II: Express Briefs, vol.55, issue.12, pp.1269-1273, 2008.
DOI : 10.1109/TCSII.2008.2008069

M. Grant and S. Boyd, CVX: Matlab software for disciplined convex programming, version 2.1, 2014.

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

O. Huber, V. Acary, B. Brogliato, and F. Plestan, Discrete-time twisting controller without numerical chattering: analysis and experimental results with an implicit method, 53rd IEEE Conference on Decision and Control, pp.129-141, 2016.
DOI : 10.1109/CDC.2014.7040071
URL : https://hal.archives-ouvertes.fr/hal-01066689

O. Huber, B. Brogliato, V. Acary, A. Boubakir, F. Plestan et al., Experimental results on implicit and explicit time-discretization of equivalent control-based sliding mode control
DOI : 10.1049/PBCE102E_ch3.2
URL : https://hal.archives-ouvertes.fr/hal-01238120

A. N. Kolmogorov and S. V. Fomin, Elements of the Theory of Funtions and Functional Analysis, 1957.

A. J. Kurdila and M. Zabarankin, Convex Functional Analysis. Systems & Control: Foundations & Applications, 2005.

A. Levant, Higher-order sliding modes, differentiation and output-feedback control, International Journal of Control, vol.76, issue.9-10, pp.924-941, 2003.
DOI : 10.1080/0020717031000099029

F. A. Miranda-villatoro and F. Castaños, Robust output regulation of variable structure systems with multivalued controls, Variable Structure Systems (VSS), 2014 13th International Workshop on, pp.1-6, 2014.

F. A. Miranda-villatoro and F. Castaños, Robust output regulation of strongly linear passive systems with multivalued maximally monotone controls. Automatic Control, IEEE Transactions

W. Perruquetti and J. Barbot, Sliding Mode Control In Engineering. Automation and Control Engineering, 2002.

J. Peypouquet and S. Sorin, Evolution equations for maximal monotone operators: asymptotic analysis in continuous and discrete time, Journal of Convex Analysis, vol.17, issue.3 4, pp.1113-1163, 2010.

A. Polyakov and A. Poznyak, Invariant ellipsoid method for minimization of unmatched disturbances effects in sliding mode control, Automatica, vol.47, issue.7, pp.1450-1454, 2011.
DOI : 10.1016/j.automatica.2011.02.013

R. T. Rockafellar, Convex Analysis. Convex Analysis, 1970.

R. T. Rockafellar and R. Wets, Variational Analysis. Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen, 2009.

Y. Shtessel, C. Edwards, L. Fridman, and A. Levant, Sliding Mode Control and Observation, 2014.
DOI : 10.1007/978-0-8176-4893-0

J. F. Sturm, Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones. Optimization methods and software, pp.625-653, 1999.

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

V. Utkin and A. Poznyak, Adaptive Sliding Mode Control, Advances in Sliding Mode Control: Concept, Theory and Implementation, pp.21-54, 2013.
DOI : 10.1007/978-3-642-36986-5_2

V. Utkin and J. Shi, Integral sliding mode in systems operating under uncertainty conditions, Proceedings of 35th IEEE Conference on Decision and Control, pp.4591-4596, 1996.
DOI : 10.1109/CDC.1996.577594

V. Utkin, J. Guldner, and J. Shi, Sliding mode control on electro-mechanical systems, Mathematical Problems in Engineering, vol.8, issue.4-5, 2009.
DOI : 10.1080/10241230306724

B. Wang, B. Brogliato, V. Acary, A. Boubakir, and F. Plestan, Experimental Comparisons Between Implicit and Explicit Implementations of Discrete-Time Sliding Mode Controllers: Toward Input and Output Chattering Suppression, IEEE Transactions on Control Systems Technology, vol.23, issue.5, pp.2071-2075, 2015.
DOI : 10.1109/TCST.2015.2396473

K. D. Young, V. I. Utkin, and U. Ozguner, A control engineer's guide to sliding mode control, IEEE Transactions on Control Systems Technology, vol.7, issue.3, pp.328-342, 1999.
DOI : 10.1109/87.761053