G. Nikolskii, On automatic stability of a ship on a given course, Proceedings of the Cenral Communication Laboratory, pp.34-75, 1934.

V. I. Utkin, Sliding Modes in Control Optimization, 1992.
DOI : 10.1007/978-3-642-84379-2

B. Hamel, ContributionàContribution`Contributionà l'´ etude mathématique des systèmes de réglage par tout ou rien, 1949.

Y. Z. Tzypkin, Theory of control relay systems, Moscow: Gostekhizdat, 1955.

S. Emelyanov, On pecularities of variable structure control systems with discontinuous switching functions, Doklady AN USSR, vol.153, pp.776-778, 1963.

J. Guldner and V. Utkin, Sliding mode control for gradient tracking and robot navigation using artificial potential fields, IEEE Transactions on Robotics and Automation, vol.11, issue.2, pp.247-254, 1995.
DOI : 10.1109/70.370505

A. Zinober, O. Ei-ghezawi, and S. Billings, Multivariable variable-structure adaptive model-following control systems, IEE Proceedings D Control Theory and Applications, vol.129, issue.1, p.6, 1982.
DOI : 10.1049/ip-d.1982.0002

S. Drakunov and V. Utkin, Sliding mode observers. Tutorial, Proceedings of 1995 34th IEEE Conference on Decision and Control, pp.3376-3378, 1995.
DOI : 10.1109/CDC.1995.479009

B. Drazenovic, The invariance conditions in variable structure systems, Automatica, vol.5, issue.3, pp.287-295, 1969.
DOI : 10.1016/0005-1098(69)90071-5

H. Sira-ramirez, Sliding regimes in general non-linear systems: a relative degree approach, International Journal of Control, vol.3, issue.4, pp.1487-1506, 1989.
DOI : 10.1016/0005-1098(69)90071-5

R. Decarlo, S. Zak, and G. Matthews, Variable structure control of nonlinear multivariable systems: a tutorial, Proceedings of the IEEE, pp.212-232, 1988.
DOI : 10.1109/5.4400

C. Edwards and S. Spurgeon, Sliding mode control: theory and applications, 1998.

W. Perruquetti and J. P. Barbot, Sliding Mode Control in Engineering, 2002.
DOI : 10.1201/9780203910856

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

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

W. Hahn, Theory and Application of Liapunov's Direct Method, E. Cliffs, 1963.

V. Haimo, Finite Time Controllers, SIAM Journal on Control and Optimization, vol.24, issue.4, pp.760-770, 1986.
DOI : 10.1137/0324047

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

S. P. Bhat and D. S. Bernstein, Lyapunov analysis of finite-time differential equations, Proceedings of 1995 American Control Conference, ACC'95, pp.1831-1832, 1995.
DOI : 10.1109/ACC.1995.531201

E. Moulay and W. Perruquetti, Finite time stability of non linear systems, IEEE Conference on Decision and Control, pp.3641-3646, 2003.

Y. 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

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

Y. Li, Y. Shen, and X. Xia, Global Finite-time Observers for a Class of Non-Lipschitz Systems, IFAC Proceedings Volumes, vol.44, issue.1, pp.703-708, 2011.
DOI : 10.3182/20110828-6-IT-1002.00798

S. P. Bhat and D. S. Bernstein, Finite-time stability of homogeneous systems, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041), pp.2513-2514, 1997.
DOI : 10.1109/ACC.1997.609245

Y. Orlov, Finite Time Stability and Quasihomogeneous Control Synthesis of Uncertain Switched Systems with Application to Underactuated Manipulators, Proceedings of the 44th IEEE Conference on Decision and Control, pp.4566-4571, 2005.
DOI : 10.1109/CDC.2005.1582882

E. Moulay and W. Perruquetti, Finite time stability and stabilization of a class of continuous systems, Journal of Mathematical Analysis and Applications, vol.323, issue.2, pp.1430-1443, 2006.
DOI : 10.1016/j.jmaa.2005.11.046

E. Moulay, Stabilization via homogeneous feedback controls, Automatica, vol.44, issue.11, pp.2981-2984, 2008.
DOI : 10.1016/j.automatica.2008.05.003

S. P. Bhat and D. S. Bernstein, Continuous, bounded, finite-time stabilization of the translational and rotational double integrators, Proceeding of the 1996 IEEE International Conference on Control Applications IEEE International Conference on Control Applications held together with IEEE International Symposium on Intelligent Control IEEE International Symposium on Computer-Aided Contro, pp.185-190, 1996.
DOI : 10.1109/CCA.1996.558628

Y. Hong, Finite-time stabilization and stabilizability of a class of controllable systems, Systems & Control Letters, vol.46, issue.4, pp.231-236, 2002.
DOI : 10.1016/S0167-6911(02)00119-6

W. Perruquetti, T. Floquet, and E. Moulay, Finite-Time Observers: Application to Secure Communication, IEEE Transactions on Automatic Control, vol.53, issue.1, pp.356-360, 2008.
DOI : 10.1109/TAC.2007.914264
URL : https://hal.archives-ouvertes.fr/inria-00176758

Y. Shen and X. Xia, Semi-global finite-time observers for nonlinear systems, Automatica, vol.44, issue.12, pp.3152-3156, 2008.
DOI : 10.1016/j.automatica.2008.05.015

Y. Shen, W. Shen, M. Jiang, and Y. Huang, Semi-global finite-time observers for multi-output nonlinear systems, International Journal of Robust and Nonlinear Control, vol.42, issue.3, pp.789-801, 2010.
DOI : 10.1002/rnc.1471

T. Menard, E. Moulay, and W. Perruquetti, A Global High-Gain Finite-Time Observer, IEEE Transactions on Automatic Control, vol.55, issue.6, pp.1500-1506, 2010.
DOI : 10.1109/TAC.2010.2045698
URL : https://hal.archives-ouvertes.fr/hal-00455790

Y. Hong, J. Huang, and Y. Xu, On an output feedback finite-time stabilization problem, IEEE Transactions on Automatic Control, vol.46, issue.2, pp.305-309, 2001.
DOI : 10.1109/9.905699

Y. Hong, Y. Xu, and J. Huang, Finite-time control for robot manipulators, Systems & Control Letters, vol.46, issue.4, pp.243-253, 2002.
DOI : 10.1016/S0167-6911(02)00130-5

E. Bernuau, W. Perruquetti, D. Efimov, and E. Moulay, Finite-time output stabilization of the double integrator, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC), pp.5906-5911
DOI : 10.1109/CDC.2012.6426565
URL : https://hal.archives-ouvertes.fr/hal-01056207

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

I. Malkin, Theory of Stability of Motion, Translation Series: Physics and Mathematics, 1952.

N. Krasovskii, Stability of Motion, 1963.

V. I. Zubov, Methods of A.M. Lyapunov and Their Applications, 1964.

W. Dayawansa and C. Martin, Some sufficient conditions for the asymptotic stabilizability of three dimensional homogeneous polynomial systems, Proceedings of the 28th IEEE Conference on Decision and Control, pp.1366-1369, 1989.
DOI : 10.1109/CDC.1989.70363

V. Zubov, On systems of ordinary differential equations with generalized homogenous right-hand sides, Izvestia vuzov. Mathematica, vol.1, pp.80-88, 1958.

H. Hermes, Nilpotent Approximations of Control Systems and Distributions, SIAM Journal on Control and Optimization, vol.24, issue.4, p.731, 1986.
DOI : 10.1137/0324045

M. Kawski, Nilpotent Lie algebras of vector fields, J. reine angew. Math, pp.1-17, 1988.

H. Hermes, Homogeneous coordinates and continuous asymptotically stabilizing feedback controls, ser. Differential Equations: Stability and Control, pp.249-260, 1991.
DOI : 10.1051/cocv:1997101
URL : http://archive.numdam.org/article/COCV_1997__2__13_0.pdf

R. Sepulchre and D. Aeyels, Stabilizability Does Not Imply Homogeneous Stabilizability for Controllable Homogeneous Systems, SIAM Journal on Control and Optimization, vol.34, issue.5, pp.1798-1813, 1996.
DOI : 10.1137/S0363012994267303

M. Kawski, GEOMETRIC HOMOGENEITY AND STABILIZATION, Proc. IFAC Nonlinear Control Symposium, pp.164-169, 1995.
DOI : 10.1016/B978-0-08-042371-5.50030-7

L. Grüne, Homogeneous state feedback stabilization of homogeneous systems, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187), pp.3409-3414, 2000.
DOI : 10.1109/CDC.2000.912230

N. Nakamura, H. Nakamura, Y. Yamashita, and H. Nishitani, Homogeneous Stabilization for Input Affine Homogeneous Systems, IEEE Transactions on Automatic Control, vol.54, issue.9
DOI : 10.1109/TAC.2009.2026865

V. Andrieu, L. Praly, and A. Astolfi, Homogeneous Approximation, Recursive Observer Design, and Output Feedback, SIAM Journal on Control and Optimization, vol.47, issue.4, pp.1814-1850, 2008.
DOI : 10.1137/060675861
URL : https://hal.archives-ouvertes.fr/hal-00362707

L. Rosier, Homogeneous Lyapunov function for homogeneous continuous vector field, Systems & Control Letters, vol.19, issue.6, pp.467-473, 1992.
DOI : 10.1016/0167-6911(92)90078-7

A. Iggidr, H. Jghima, and R. Outbib, Global stabilization of planar homogeneous polynomial systems, Nonlinear Analysis: Theory, Methods & Applications, vol.34, issue.7, pp.1097-1109, 1998.
DOI : 10.1016/S0362-546X(98)00030-3

A. Anta, To Sample or not to Sample: Self-Triggered Control for Nonlinear Systems, IEEE Transactions on Automatic Control, vol.55, issue.9, pp.2030-2042, 2010.
DOI : 10.1109/TAC.2010.2042980

D. Efimov and W. Perruquetti, Oscillations Conditions in Homogenous Systems, Proc. IFAC NOLCOS Symp, pp.1379-1384, 2010.
DOI : 10.3182/20100901-3-IT-2016.00101
URL : https://hal.archives-ouvertes.fr/hal-00561003

L. Praly, Generalized weighted homogeneity and state dependent time scale for linear controllable systems, Proceedings of the 36th IEEE Conference on Decision and Control, pp.4342-4347, 1997.
DOI : 10.1109/CDC.1997.649536

V. V. Khomenuk, On systems of ordinary differential equations with generalized homogenous right-hand sides, Izvestia vuzov. Mathematica, vol.3, issue.22, pp.157-164, 1961.

M. Kawski, Nonlinear control and combinatorics of words, " in Geometry of Feedback and Optimal Control, pp.305-346, 1998.

L. Rosier, Etude de quelquesprobì emes de stabilisation, 1993.

A. Levant, Quasi-continuous high-order sliding-mode controllers, IEEE Transactions on Automatic Control, vol.50, issue.11, pp.1812-1816, 2005.
DOI : 10.1109/TAC.2005.858646
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.218.4061

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

J. Aubin and A. Cellina, Differential Inclusions, ser, Grundlehren der Math. Wiisenschaften, vol.264, 1984.

J. Aubin and H. Frankowska, Set-Valued Analysis, ser. System & Control: Foundations & Applications, 1990.

F. Clarke, Y. Ledyaev, R. Stern, and P. Wolenski, Non Smooth Analysis and Application, ser. Graduate Texts in Mathematics, 1997.

H. K. Khalil, Nonlinear Systems, ser. NJ 07458. Upper Saddle River, 1996.

A. Levant, Homogeneity approach to high-order sliding mode design, Automatica, vol.41, issue.5, pp.823-830, 2005.
DOI : 10.1016/j.automatica.2004.11.029

E. Bernuau, A. Polyakov, D. Efimov, and W. Perruquetti, On extension of homogeneity notion for differential inclusions, Proceeding of the European Control Conference, pp.2204-2209, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00801818

A. Polyakov, On settling time function and stability of vector relay systems, 2012 12th International Workshop on Variable Structure Systems, pp.149-154
DOI : 10.1109/VSS.2012.6163493

G. Kamenkov, On stability of motion over a finite interval of time, Journal of Applied Math. and Mechanics (PMM), vol.17, pp.529-540, 1953.

A. Lebedev, The problem of stability in a finite interval of time, Journal of Applied Math. and Mechanics (PMM), vol.18, pp.75-94, 1954.

L. Weiss and E. Infante, ON THE STABILITY OF SYSTEMS DEFINED OVER A FINITE TIME INTERVAL, Proc. of the National Academy of Sciences, pp.440-448, 1965.
DOI : 10.1073/pnas.54.1.44

P. Dorato, An overview of finite-time stability, " in Current Trends in Nonlinear Systems and Control, ser. Systems & Control: Foundations & Applications, pp.185-194, 2006.

E. Moulay and W. Perruquetti, Finite-Time Stability and Stabilization:State of the art, ser. LNCIS, pp.23-41, 2006.

A. Polyakov, Nonlinear Feedback Design for Fixed-Time Stabilization of Linear Control Systems, IEEE Transactions on Automatic Control, vol.57, issue.8, pp.2106-2110, 2012.
DOI : 10.1109/TAC.2011.2179869
URL : https://hal.archives-ouvertes.fr/hal-00757561

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

E. Moulay and W. Perruquetti, Finite time stability of differential inclusions, IMA Journal of Mathematical Control and Information, vol.22, issue.4, pp.465-475, 2005.
DOI : 10.1093/imamci/dni039

H. Yiguang, J. Zhong-ping, and F. Gang, Finite-time input-to-state stability and applications to finite-time control design, SIAM J. Control Optim, vol.48, issue.7, pp.4395-4418

S. Dashkovskiy, D. Efimov, and E. Sontag, Input to state stability and allied system properties, Automation and Remote Control, vol.72, issue.8, pp.1579-1614, 2011.
DOI : 10.1134/S0005117911080017
URL : https://hal.archives-ouvertes.fr/hal-00639491

W. 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

M. Xiaowu, G. Yang, and Z. Wei, Integral input-to-state stability for one class of discontinuous dynamical systems, 29th Chinese Control Conference (CCC), pp.912-914, 2010.

E. Bernuau, A. Polyakov, D. Efimov, and W. Perruquetti, Robustness of finite-time stability property for sliding modes, Proc. of 5th IFAC Symposium on System Structure and Control, pp.4-6, 2013.
DOI : 10.3182/20130204-3-FR-2033.00159
URL : https://hal.archives-ouvertes.fr/hal-00745673

E. Ryan, Universal stabilization of a class of nonlinear systems with homogeneous vector fields, Systems & Control Letters, vol.26, issue.3, pp.177-184, 1995.
DOI : 10.1016/0167-6911(95)00013-Y

Y. Hong, H??? control, stabilization, and input???output stability of nonlinear systems with homogeneous properties, Automatica, vol.37, issue.6, pp.819-829, 2001.
DOI : 10.1016/S0005-1098(01)00027-9

E. Bernuau, A. Polyakov, D. Efimov, and W. Perruquetti, Verification of ISS, iISS and IOSS properties applying weighted homogeneity, Systems & Control Letters, vol.62, issue.12, pp.1159-1167, 2013.
DOI : 10.1016/j.sysconle.2013.09.004
URL : https://hal.archives-ouvertes.fr/hal-00877148

L. Fridman, Sliding Mode Enforcement after 1990: Main Results and Some Open Problems, pp.3-57, 2011.
DOI : 10.1007/978-3-642-22164-4_1

A. Poznyak, A. Polyakov, and V. Strygin, Analysis of finite-time convergence by the method of Lyapunov functions in systems with second-order sliding modes, Journal of Applied Mathematics and Mechanics, vol.75, issue.3, pp.289-303, 2011.
DOI : 10.1016/j.jappmathmech.2011.07.006

Z. Man and X. Yu, Terminal sliding mode control of mimo linear systems, IEEE Transactions on Circuits and Systems: Part I, issue.11, pp.1065-1070, 1997.

Y. Feng, X. Yu, and Z. Man, Non-singular terminal sliding mode control of rigid manipulators, Automatica, vol.38, issue.12, pp.2159-2167, 2002.
DOI : 10.1016/S0005-1098(02)00147-4

X. Yu and Z. Man, Fast terminal sliding mode control design for nonlinear dynamic systems, IEEE Transactions on Circuits and Systems -Part I, vol.39, issue.2, pp.261-264, 2002.

G. Bartolini, A. Ferrara, and E. Usai, Chattering avoidance by second-order sliding mode control, IEEE Transactions on Automatic Control, vol.43, issue.2, pp.241-246, 1998.
DOI : 10.1109/9.661074

I. Boiko and L. Fridman, Analysis of chattering in continuous sliding-mode controllers, IEEE Transactions on Automatic Control, vol.50, issue.9, pp.1442-1446, 2005.
DOI : 10.1109/TAC.2005.854655

A. Levant, Chattering Analysis, IEEE Transactions on Automatic Control, vol.55, issue.6, pp.1380-1389, 2010.
DOI : 10.1109/TAC.2010.2041973

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. Levant, Principles of 2-sliding mode design, Automatica, vol.43, issue.4, pp.576-586, 2007.
DOI : 10.1016/j.automatica.2006.10.008

J. Moreno and A. 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. Cruz-zavala, J. Moreno, and L. Fridman, Uniform Robust Exact Differentiator, IEEE Transactions on Automatic Control, vol.56, issue.11, pp.2727-2733, 2011.
DOI : 10.1109/TAC.2011.2160030