M. A. Aizerman and E. S. Pyatnitskii, Foundations of theory of discontinuous systems i. Automation and Remote Control, pp.1066-1079, 1974.

A. Bacciotti and F. Ceragioli, Nonpathological Lyapunov functions and discontinuous Carath??odory systems, Automatica, vol.42, issue.3, pp.453-458, 2006.
DOI : 10.1016/j.automatica.2005.10.014

A. Bacciotti and L. Rosier, Lyapunov Functions and Stability in Control Theory, 2005.

E. A. Barbashin, Lyapunov Functions, Moscow:Nauka [in Russian], 1970.

G. Bartolini and T. Zolezzi, Variable structure systems nonlinear in the control law, IEEE Transactions on Automatic Control, vol.30, issue.7, pp.681-684, 1985.
DOI : 10.1109/TAC.1985.1104025

S. P. Bhat and D. S. Bernstein, Finite-Time Stability of Continuous Autonomous Systems, SIAM Journal on Control and Optimization, vol.38, issue.3, pp.751-766, 2000.
DOI : 10.1137/S0363012997321358

I. Boiko, Discontinuous control systems : frequencydomain analysis and design, 2009.

V. Chellaboina, A. Leonessa, and W. Haddad, Generalized Lyapunov and invariant set theorems for nonlinear dynamical systems, Systems & Control Letters, vol.38, issue.4-5, pp.289-295, 1999.
DOI : 10.1016/S0167-6911(99)00076-6

S. B. Choi and J. K. Hedrick, Robust Throttle Control of Automotive Engines: Theory and Experiment, Journal of Dynamic Systems, Measurement, and Control, vol.118, issue.1, pp.92-98, 1996.
DOI : 10.1115/1.2801156

Y. S. Clarke, R. Ledyaev, P. Stern, and . Wolenski, Qualitative properties of trajectories of control systems: A survey, Journal of Dynamical and Control Systems, vol.20, issue.No. 2, pp.1-48, 1995.
DOI : 10.1007/BF02254655

F. H. Clarke, Y. S. Ledyaev, and R. J. Stern, Asymptotic Stability and Smooth Lyapunov Functions, Journal of Differential Equations, vol.149, issue.1, pp.69-114, 1998.
DOI : 10.1006/jdeq.1998.3476

A. F. Filippov, Differential Equations with Discontinuous Righthand Sides, 1988.
DOI : 10.1007/978-94-015-7793-9

. Flugge-lotz, Discontinuous automatic control, 1953.
DOI : 10.1515/9781400877218

. Hahn, Stability of Motion, 1967.
DOI : 10.1007/978-3-642-50085-5

W. P. Heemels and S. Weiland, Input-to-state stability and interconnections of discontinuous dynamical systems, Automatica, vol.44, issue.12, pp.3079-3086, 2008.
DOI : 10.1016/j.automatica.2008.04.025

A. Levant, 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

A. M. Lyapunov, The general problem of the stability of motion, 1992.

B. S. Mordukhovich, Variational Analysis and Generalized Differentiation I: Basic Theory, 2006.
DOI : 10.1007/3-540-31247-1

J. Moreno and M. Osorio, 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

E. Moulay and W. Perruquetti, Finite time stability conditions for non-autonomous continuous systems, International Journal of Control, vol.55, issue.5, pp.797-803, 2008.
DOI : 10.1080/00207177908922792

URL : https://hal.archives-ouvertes.fr/hal-00177572

I. P. Natanson, Theory of functions of a real variable, 1955.

Y. I. Neimark, Note on A. Filippov paper, Proceedings of 1st IFAC Congress II. Butterworths, 1961.

. Orlov, 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

A. Polyakov and A. Poznyak, Lyapunov function design for finite-time convergence analysis: ???Twisting??? controller for second-order sliding mode realization, Automatica, vol.45, issue.2, pp.444-448, 2009.
DOI : 10.1016/j.automatica.2008.07.013

A. Polyakov and A. Poznyak, 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

A. Polyakov and A. Poznyak, Unified Lyapunov function for a finite-time stability analysis of relay second-order sliding mode control systems, IMA Journal of Mathematical Control and Information, vol.29, issue.4, pp.529-550, 2012.
DOI : 10.1093/imamci/dns007

A. S. Poznyak, Advanced Mathematical Tools for Automatic Control Engineers, 2008.

E. Roxin, On finite stability in control systems, Rendiconti del Circolo Matematico di Palermo, vol.XV, issue.3, pp.273-283, 1966.
DOI : 10.1007/BF02844106

D. Shevitz and B. Paden, Lyapunov stability theory of nonsmooth systems, IEEE Transactions on Automatic Control, vol.39, issue.9, pp.1910-1914, 1994.
DOI : 10.1109/9.317122

Y. Z. Tsypkin, Relay Control Systems, 1984.

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

R. E. Vinograd, The inadequacy of the method of characteristic exponents for the study of nonlinear differential equations, Math. Sbornik, issue.83, pp.41431-438, 1957.

S. C. Zaremba, Sur une extension de la notion d'equation differentiel, Comptes Rendus Acad. Sc, vol.199, pp.545-548, 1934.

Q. J. Zhu, Lower semicontinuous Lyapunov functions and subdifferential calculus, Proceedings of the 41st IEEE Conference on Decision and Control, 2002., 2002.
DOI : 10.1109/CDC.2002.1184589