A REVIEW ON STABILITY OF SWITCHED SYSTEMS FOR ARBITRARY SWITCHINGS

In this paper we review some recent results on stability of multilinear switched systems, under arbitrary switchings. An open problems is stated.

[1]  Robert Vallée,et al.  Analysis and Decision Making in Uncertain Systems , 2006 .

[2]  Ugo Boscain,et al.  Stability of planar nonlinear switched systems , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[3]  U. Boscain.  Stability of planar switched systems: the linear single, input case , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[4]  Robert Shorten,et al.  Necessary and sufficient conditions for the existence of a common quadratic Lyapunov function for a finite number of stable second order linear time‐invariant systems , 2002 .

[5]  Clyde F. Martin,et al.  A Converse Lyapunov Theorem for a Class of Dynamical Systems which Undergo Switching , 1999, IEEE Transactions on Automatic Control.

[6]  F. Blanchini,et al.  A new class of universal Lyapunov functions for the control of uncertain linear systems , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

[7]  Graziano Chesi,et al.  Homogeneous Lyapunov functions for systems with structured uncertainties , 2003, Autom..

[8]  R.N. Shorten,et al.  Necessary and sufficient conditions for the existence of a common quadratic Lyapunov function for two stable second order linear time-invariant systems , 1999, Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251).

[9]  A. Morse,et al.  Stability of switched systems: a Lie-algebraic condition ( , 1999 .

[10]  A. Macintyre,et al.  The Elementary Theory of Restricted Analytic Fields with Exponentiation , 1994 .

[11]  A. Morse,et al.  Basic problems in stability and design of switched systems , 1999 .

[12]  Daniel Liberzon,et al.  Switching in Systems and Control , 2003, Systems & Control: Foundations & Applications.

[13]  A. L. Zelentsovsky.  Nonquadratic Lyapunov functions for robust stability analysis of linear uncertain systems , 1994, IEEE Trans. Autom. Control..

[14]  Jean-Marie Lion,et al.  Théorème de préparation pour les fonctions logarithmico-exponentielles , 1997 .

[15]  Daniel Liberzon,et al.  Lie-Algebraic Stability Criteria for Switched Systems , 2001, SIAM J. Control. Optim..

[16]  Franco Blanchini,et al.  Nonquadratic Lyapunov functions for robust control , 1995, Autom..

[17]  B. Piccoli,et al.  Optimal Syntheses for Control Systems on 2-D Manifolds , 2004 .

[18]  David Angeli,et al.  Uniform Global Asymptotic Stability of Differential Inclusions , 2004 .

[19]  Y. Pyatnitskiy,et al.  Criteria of asymptotic stability of differential and difference inclusions encountered in control theory , 1989 .

[20]  A. Olas.  On robustness of systems with structured uncertainties , 1992 .

[21]  Yacine Chitour,et al.  Common Polynomial Lyapunov Functions for Linear Switched Systems , 2006, SIAM J. Control. Optim..