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
Discrete-Time Terminal Sliding Mode Control Systems Based on Euler's Discretization, IEEE Transactions on Automatic Control, vol.59, issue.2, pp.546-552, 2014. ,
DOI : 10.1109/TAC.2013.2273267
Euler???s discretization effect on a twisting algorithm based sliding mode control, Automatica, vol.68, pp.203-208, 2016. ,
DOI : 10.1016/j.automatica.2016.01.051
Experimental results on implicit and explicit time-discretization of equivalent-control-based sliding-mode control, " in Recent Trends in Sliding Mode Control, ser. Control, Robotics and Sensors, pp.207-235, 2016. ,
Classification of Hidden Dynamics in Discontinuous Dynamical Systems, SIAM Journal on Applied Dynamical Systems, vol.14, issue.3, pp.1454-1477, 2015. ,
DOI : 10.1137/15100326X
Sliding modes in intersecting switching surfaces. I. Blending, Houston J. Math, vol.24, pp.545-569, 1998. ,
Regularizing Piecewise Smooth Differential Systems: Co-Dimension $$2$$ Discontinuity Surface, Journal of Dynamics and Differential Equations, vol.62, issue.10, pp.71-94, 2013. ,
DOI : 10.1016/j.apnum.2012.06.021
On the Equivalence between the Sigmoidal Approach and Utkin's Approach for Piecewise-Linear Models of Gene Regulatory Networks, SIAM Journal on Applied Dynamical Systems, vol.13, issue.3, pp.1270-1292, 2014. ,
DOI : 10.1137/130950483
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
Chattering-Free Digital Sliding-Mode Control With State Observer and Disturbance Rejection, IEEE Transactions on Automatic Control, vol.57, issue.5, pp.1087-1101, 2012. ,
DOI : 10.1109/TAC.2011.2174676
URL : https://hal.archives-ouvertes.fr/inria-00494417
Implicit discrete-time twisting controller without numerical chattering: Analysis and experimental results, Control Engineering Practice, vol.46, pp.129-141, 2016. ,
DOI : 10.1016/j.conengprac.2015.10.013
URL : https://hal.archives-ouvertes.fr/hal-01066689
Lyapunov Stability and Performance Analysis of the Implicit Discrete Sliding Mode Control, IEEE Transactions on Automatic Control, vol.61, issue.10, pp.3016-3030, 2016. ,
DOI : 10.1109/TAC.2015.2506991
URL : https://hal.archives-ouvertes.fr/hal-01236159
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
Proxy-Based Sliding Mode Control: A Safer Extension of PID Position Control, IEEE Transactions on Robotics, vol.26, issue.4, pp.670-683, 2010. ,
DOI : 10.1109/TRO.2010.2051188
Globally stable implicit Euler time-discretization of a nonlinear single-input sliding-mode control system, 2015 54th IEEE Conference on Decision and Control (CDC), pp.5426-5431, 2015. ,
DOI : 10.1109/CDC.2015.7403069
URL : https://hal.archives-ouvertes.fr/hal-01212601
Multivalued Robust Tracking Control of Lagrange Systems: Continuous and Discrete-Time Algorithms, IEEE Transactions on Automatic Control, vol.62, issue.9, pp.4436-4450, 2017. ,
DOI : 10.1109/TAC.2017.2662804
URL : https://hal.archives-ouvertes.fr/hal-01254303
On fixed and finite time stability in sliding mode control, 52nd IEEE Conference on Decision and Control, pp.4260-4265, 2013. ,
DOI : 10.1109/CDC.2013.6760544
Realization and Discretization of Asymptotically Stable Homogeneous Systems, IEEE Transactions on Automatic Control, 2017. ,
DOI : 10.1109/TAC.2017.2699284
URL : https://hal.archives-ouvertes.fr/hal-01514350
Sliding order and sliding accuracy in sliding mode control, International Journal of Control, vol.51, issue.6, pp.1247-1263, 1993. ,
DOI : 10.1109/TAC.1977.1101661
Higher-order sliding modes in binary control systems, Soviet Physics Doklady, vol.31, issue.31, p.291, 1986. ,
Finite Time Stability and Robust Control Synthesis of Uncertain Switched Systems, SIAM Journal on Control and Optimization, vol.43, issue.4, pp.1253-1271, 2005. ,
DOI : 10.1137/S0363012903425593
Strict Lyapunov Functions for the Super-Twisting Algorithm, IEEE Transactions on Automatic Control, vol.57, issue.4, pp.1035-1040, 2012. ,
DOI : 10.1109/TAC.2012.2186179
Reaching Time Estimation for “Super-Twisting” Second Order Sliding Mode Controller via Lyapunov Function Designing, IEEE Transactions on Automatic Control, vol.54, issue.8, pp.1951-1955, 2009. ,
DOI : 10.1109/TAC.2009.2023781
Implementation of Super-Twisting Control: Super-Twisting and Higher Order Sliding-Mode Observer-Based Approaches, IEEE Transactions on Industrial Electronics, vol.63, issue.6, pp.3677-3685, 2016. ,
DOI : 10.1109/TIE.2016.2523913
Analysis and implementation of discrete-time sliding mode control, 2015. ,
URL : https://hal.archives-ouvertes.fr/tel-01194430
Finite-Dimensional Variational Inequalities and Complementarity Problems, Volume I, ser. Springer Series in Operations Research, 2003. ,
Variational Analysis, ser. Grundlehren der mathematischen Wissenschaften, 2009. ,
The Linear Complementarity Problem, ser, Classics in Applied Mathematics. Philadelphia: Society for Industrial Mathematics, issue.60, 2009. ,
Convex Analysis, 1997. ,
DOI : 10.1515/9781400873173
A decomposition property for a class of square matrices, Applied Mathematics Letters, vol.4, issue.5, pp.67-69, 1991. ,
DOI : 10.1016/0893-9659(91)90148-O
Fundamentals of Convex Analysis, ser. Grundlehren Text Editions APPENDIX Definition 2. [31] Given a set K ? R n and a mapping F : K ? R n , the variational inequality V I(K, F ) is defined as: Find a vector x ? K such that y ? x, F (x) ? 0 for all y ? K. When F ( · ) is the affine function F (x) = M x + q, this is an affine variational inequality (AVI), 2001. ,