K. Aaaaa, J. Xx, and Y. Xxxxxxx, On the discrete-time integral sliding-mode control, Automatic Control, IEEE Transactions on, vol.52, pp.709-715, 2007.

V. Aaaa, B. Bbbbbbb, O. Hhhhh, and F. Pppppppp, An introduction to SSSSSSS, Rapport Technique RT-0340

V. and A. B. Bb, Numerical Methods for Nonsmooth Dynamical Systems: Applications in Mechanics and Electronics, of Lecture Notes in Applied and Computational Mechanics, 2008.

V. and A. B. Bb, Implicit Euler numerical scheme and chatteringfree implementation of sliding mode systems, Systems & Control Letters, vol.59, issue.159, pp.284-293, 2010.

V. Aaaa, B. Bb, and Y. Oooo, Chattering-free digital sliding-mode control with state observer and disturbance rejection, Automatic Control, IEEE Transactions on, vol.57, issue.159, pp.1087-1101, 2012.

J. and A. V. Uuuuu, Sliding mode control design based on Ackermann's formula, Automatic Control, IEEE Transactions on, vol.43, pp.234-237, 1998.

M. A. Aaaaaaaa-f and . Gggggggggg, On certain switching speciics in nonlinear automatic control systems with a piecewise-smooth characteristics of nonlinear element, pp.1017-1028, 1957.

M. A. Aaaaaaaa-y and . Ppp, Fundamentals of the theory of discontinuous systems. I, Avtomatika i Telemekhanika, pp.33-47, 1974.

M. A. Aaaaaaaa-y and . Ppp, Fundamentals of the theory of discontinuous systems. II, Avtomatika i Telemekhanika, pp.39-61, 1974.

L. Aaaa, N. Ffff, and D. , P, Functions of Bounded Variation and Free Discontinuity Problems, p.178, 2000.

J. and A. P. Ssssss, Über stückweise lineare Diierentialgleichungen, die bei Regelungsproblemen auftreten I, Archiv der Mathematik, vol.7, pp.148-156, 1956.

J. and A. P. Ssssss, Über stückweise lineare Diierentialgleichungen, die bei Regelungsproblemen auftreten II, Archiv der Mathematik, vol.7, pp.157-164, 1956.

J. and B. M. Ssss, Numerical precision for diierential inclusions with uniqueness, Mathematical Modelling and Numerical Analysis, pp.427-460, 2002.

V. Bb, HEM5 user's guide, technical report, 1994.

B. Bb, Nonsmooth Mechanics: Models, Dynamics and Control, Communications and Control Engineering, 1999.

B. Bb, Absolute stability and the lagrange-dirichlet theorem with monotone multivalued mappings, Systems & control letters, vol.51, pp.343-353, 2004.

B. Bb, O. Eeeeeee, R. Llllll, and B. Mm, Dissipative Systems Analysis and Control: Theory and Applications, Communications and Control Engineering, 2007.

K. Çççççççç, Complementarity Methods in the Analysis of Piecewise Linear Dynamical Systems, 2001.

K. Çççççççç, W. Hhhhhhh, and J. M. Ssssss, Consistency of a timestepping method for a class of piecewise-linear networks, Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on, vol.49, pp.349-357, 2002.

K. Çççççççç, W. Hhhhhhh, and J. M. Ssssss, On linear passive complementarity systems, European Journal of Control, vol.8, pp.220-237, 2002.

M. Cc, Piecewise Linear Homotopies and AAne Variational Inequalities, 1994.

M. and C. M. Ffffff, A pivotal method for aane variational inequalities, Mathematics of Operations Research, vol.21, pp.44-64, 1996.

R. Cccccc, A eld guide to the matrix classes found in the literature of the linear complementarity problem, Journal of Global Optimization, vol.46, pp.571-580, 2010.

R. Cccccc, J. P. , and R. Ss, The Linear Complementarity Problem, no, Classics in Applied Mathematics, pp.52-98, 2009.

A. and D. F. Llllll, Diierence methods for diierential inclusions: a survey, SIAM Review, pp.263-294, 1992.

S. and D. V. Uuuuu, On discrete-time sliding modes, Proc. of IFAC Nonlinear Control System Design Conf, pp.273-278, 1989.

B. Dd, The invariance conditions in variable structure systems, Automatica, vol.5, pp.287-295, 1969.

B. C. Ee, A short course in solving equations with pl homotopies, pp.73-143, 1976.

C. and E. S. Ssss, Sliding Mode Control, of Systems and Control Book Series, p.72, 1998.

S. V. Eeee-''''', S. K. Kkk, and L. V. Lll, Higher-order sliding modes in binary control systems, Soviet Physics Doklady, p.291, 1986.

A. F. Fffffff, Diierential equations with discontinuous right-hand side, Matematicheskii Sbornik, pp.99-128, 1960.

I. Ffffff-llll, Discontinuous Automatic Control, 1953.

B. Fffffff, Generation of nite diierence formulas on arbitrarily spaced grids, Mathematics of Computation, vol.51, pp.699-706, 1988.

L. Fffffff, An averaging approach to chattering, Automatic Control, IEEE Transactions on, vol.46, pp.1260-1265, 2001.

K. Fffff, Sliding mode control of a discrete system, Systems & Control Letters, vol.14, issue.38, pp.145-152, 1990.

W. Gg, Y. W. , and A. Hhhhhh, Discrete-time variable structure control systems, Industrial Electronics, IEEE Transactions on, vol.42, pp.117-122, 1995.

G. Gggg-?-c and . Mmmmmm, Robust discrete-time chattering free sliding mode control, Systems & Control Letters, pp.41-60, 2000.

E. Hhhhhh, S. P. Nnn, and G. W. , Solving Ordinary Diierential Equations I: Nonstii Problems, of Springer Series in Computational Mathematics, p.14, 1993.

I. Hh, Ü. Ööööööö, and V. Uuuuu, On sliding mode observers via equivalent control approach, International Journal of Control, vol.71, pp.1051-1067, 1998.

L. and H. E. Fffffff, Robust sampled?data control of switched aane systems , Automatic Control, IEEE Transactions on, vol.58, pp.2922-2928, 2013.

L. Hhhhh, E. Fffffff, and T. Fffffff, Variable structure control with generalized relays: A simple convex optimization approach, Automatic Control, IEEE Transactions on, vol.60, pp.497-502, 2015.

A. C. Hhhhhhh, ODEPACK, a systematized collection of ODE solvers, pp.55-64, 1983.

D. and H. A. Pppp, Mathematical Systems Theory I, of Texts in Applied Mathematics, 2005.

J. Hhhhhh-uuuuuu-c and . Llllllllll, Fundamentals of Convex Analysis, Grundlehren Text Editions, 2001.

R. A. Hhhh-c and . Jjjjjjj, Topics in Matrix Analysis, 1991.

D. and H. P. Lllll, Linear matrix equations from an inverse problem of vibration theory, Linear Algebra and its Applications, vol.246, pp.31-47, 1996.

S. and H. S. ???, On discrete-time variable structure sliding mode control, Systems & Control Letters, vol.38, pp.283-288, 1999.

J. D. Hhhh, Matplotlib: a 2D graphics environment, Computing in Science & Engineering, pp.90-95, 2007.

U. Iiiii, Control Systems of Variable Structure, 1976.

M. and J. J. Mmmmm, Dynamics in the presence of unilateral contacts and dry friction: A numerical approach, in Unilateral Problems in Structural Analysis, International Centre for Mechanical Sciences, pp.151-196, 1987.

E. Jjjjj, T. Oooooooo, and P. Ppppp, SciPy: Open source scientiic tools for Python

A. Kk-mmmmmmm, Implicit Runge-Kutta methods for diierential inclusions, Numerical Functional Analysis and Optimization, pp.11-937, 1990.

A. Kk-mmmmmmm, The implicit midpoint rule applied to discontinuous differential equations, Computing, pp.49-94, 1992.

C. G. Kkk-s and . Mmmm, Hermitian and nonnegative deenite solutions of linear matrix equations, SIAM Journal on Applied Mathematics, pp.31-579, 1976.

A. A. Kkkkkkkkk and . Zzzzzzz, Sliding mode control of discrete-time systems, Journal of Dynamic Systems, Measurement, and Control, vol.122, p.793, 2000.

U. Kkkk, S. Ssssssss, Y. Iiiii, and . Comments-on, On the stability od discrete-time sliding mode control systems, Automatic Control IEEE Transactions on, vol.34, pp.1021-1022, 1989.

N. Lll, C. Ee, and S. Ssss, On output tracking using dynamic output feedback discrete-time sliding-mode controllers, Automatic Control, IEEE Transactions on, vol.52, pp.1975-1981, 2007.

F. Llllll, Euler's method revisited, Proc. Steklov Inst, pp.473-494, 1995.

A. Lll, Sliding order and sliding accuracy in sliding mode control, International Journal of Control, vol.58, pp.1247-1263, 1993.

A. Lll, Robust exact diierentiation via sliding mode technique, Automatica, vol.34, pp.379-384, 1998.

A. Lll, Higher-order sliding modes, diierentiation and output-feedback control, International Journal of Control, vol.76, pp.924-941, 2003.

A. Lll, Chattering analysis, Automatic Control, IEEE Transactions, vol.55, pp.1380-1389, 2010.

Q. Ll, Large-Scale Computing for Complementarity and Variational Inequalities, 2010.

C. Ss, A total chattering-free sliding mode control for sampleddata systems, American Control Conference, Proceedings of the 2004, pp.1940-1945, 2004.

M. Llllllllll, B. Dd, ?. C. Mmmmmm, and B. , Disturbance compensation in digital sliding mode, EUROCON-International Conference on Computer as a Tool (EUROCON), pp.1-4, 2011.

Y. Llll, A. V. Ssssss, and K. Çççççççç, Uniqueness of solutions of linear relay systems, Automatica, pp.35-467, 1999.

Z. P. Lll, A decomposition property for a class of square matrices, Applied Mathematics Letters, vol.4, pp.67-69, 1991.

D. Mmmmm-?-c and . Mmmmmm, Sliding mode-based minimum variance and generalized minimum variance controls with (T ) and (T ) accuracy, Electrical Engineering (Archiv fur Elektrotechnik), pp.229-237, 2004.

C. and M. C. Ll, Nineteen dubious ways to compute the exponential of a matrix, twenty--ve years later, SIAM Review, vol.45, pp.3-49, 2003.

J. J. Mmmmm, Unilateral contact and dry friction in nite freedom dynamics, Nonsmooth Mechanics and Applications of International Centre for Mechanical Sciences, pp.1-82, 1988.

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

F. and P. C. Ggggggg, Multibody Dynamics with Unilateral Contacts, Wiley Series in Nonlinear Science, 1996.

R. R. Pppppp, W. Hhhhhhh, and H. Nnnnnnnnn, Lectures on Maximal Monotone Operators, arXiv:math/9302209 [math.FA] On solution concepts and wellposedness of linear relay systems, Automatica, pp.39-2139, 1993.

S. Qq, X. Xxx, and J. Zzzzz, Dynamical behaviors of an Euler discretized sliding mode control systems, Automatic Control, IEEE Transactions on, vol.59, pp.2525-2529, 2014.

R. T. Rrrrrrrrrrr, Convex Analysis, 1997.

J. Rrrrr, Error analysis for implicit approximations to solutions to Cauchy problems, SIAM Journal on Numerical Analysis, vol.33, issue.39, pp.68-87, 1996.

S. Ssssssss, Y. Iiiii, and O. Kkkkkk, On the stability of discretetime sliding mode control systems, Automatic Control IEEE Transactions on, vol.32, pp.930-932, 1987.

S. and S. S. Ssss, Static characteristics of a three way electropneumatic servovalve, Proceedings of the 12th Conference on Fluid Power Technology, pp.643-645, 1996.

Y. Ssssssss, C. Ee, L. Fffffff, and A. Lll, Sliding Mode Control and Observation, Control Engineering

Y. Ssssssss, M. T. , and F. Ppppp, A novel adaptive-gain supertwisting sliding mode controller: Methodology and application, Automatica, pp.48-759, 2012.

H. Sss-rrrr, Non-linear discrete variable structure systems in quasi-sliding mode, International Journal of control, vol.54, pp.1171-1187, 1991.

E. Ssss, Mathematical Control Theory: Deterministic Finite Dimensional Systems, of Textbooks in Applied Mathematics, 1998.

W. Ss, S. Dd, and Ü. Ööööööö, Implementation of variable structure control for sampled-data systems, Robust Control via Variable Structure and Lyapunov Techniques, pp.87-106, 1996.

W. Ss, S. Dd, and Ü. Ööööööö, An O(T ) boundary layer in sliding mode for sampled-data systems, Automatic Control, IEEE Transactions on, vol.45, pp.482-485, 2000.

V. Uuuuu, Variable structure systems with sliding modes, Automatic Control, IEEE Transactions on, vol.22, pp.212-222, 1977.

V. Uuuuu, Sliding Modes in Control and Optimization, Communications and Control Engineering, p.38, 1992.

V. Uuuuu, Sliding mode control in discrete-time and diierence systems, Variable Structure and Lyapunov Control, pp.87-107, 1994.

V. and U. H. Lll, The chattering analysis, in Power Electronics and Motion Control Conference, EPE-PEMC 12th International, IEEE, pp.2014-2019, 2006.

B. and W. S. ???, Observation of dynamical systems in the presence of bounded nonlinearities/uncertainties, in Decision and Control, 25th IEEE Conference on, pp.961-966, 1986.

B. W. , B. Bb, V. Aaaa, A. Bbbbbbbb, and F. Ppppp, Experimental comparisons between implicit and explicit implementations of discrete-time sliding mode controllers: Towards chattering suppression in output and input signals, Variable Structure Systems (VSS), 2014 13th International Workshop on, pp.1-6, 2014.

B. W. , B. Bb, V. Aaaa, A. Bbbbbbbb, and F. Ppppp, Comparisons between implicit and explicit discrete-time implementations of equivalentcontrol-based sliding mode controllers: input and output chattering suppression via the implicit method, Control Systems Technology, IEEE Transactions on, p.p. in press, 2015.

B. W. , X. Y. , and X. Ll, ZOH discretization eeect on higher-order sliding-mode control systems, Industrial Electronics, IEEE Transactions on, vol.55, pp.4055-4064, 2008.

X. Y. , B. W. , Z. Ggggg, and G. Cccc, Discretization eeect on equivalent control-based multi-input sliding-mode control systems, Automatic Control, IEEE Transactions on, vol.53, pp.1563-1569, 2008.