Stabilization of a class switched linear systems

This paper studies periodic stabilization of a class of switched linear systems. The concepts of periodically asymptotical stabilizability (PAS) and periodically exponential stabilizability (PES) are first introduced. First, for the continuous-time case, a necessary and sufficient condition for PAS is established. Then, it is proved that PES is equivalent to PAS, and controllability is equivalent to PES with arbitrary decaying rate, respectively. The corresponding algorithms are given as well. Finally, a numerical examples are given to illustrate our results.

[1]  Guangming Xie,et al.  Necessary and sufficient conditions for controllability of switched linear systems , 2002, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301).

[2]  A. Michel,et al.  Stability theory for hybrid dynamical systems , 1998, IEEE Trans. Autom. Control..

[3]  Shuzhi Sam Ge,et al.  Reachability and controllability of switched linear discrete-time systems , 2001, IEEE Trans. Autom. Control..

[4]  Guangming Xie,et al.  Controllability of switched linear systems , 2002, IEEE Trans. Autom. Control..

[5]  Zhengguo Li,et al.  Stabilization of a class of switched systems via designing switching laws , 2001, IEEE Trans. Autom. Control..

[6]  Robin J. Evans,et al.  Stability results for switched controller systems , 1999, Autom..

[7]  K. Narendra,et al.  A common Lyapunov function for stable LTI systems with commuting A-matrices , 1994, IEEE Trans. Autom. Control..

[8]  Panos J. Antsaklis,et al.  Design of stabilizing control laws for second-order switched systems , 1999 .

[9]  S. Pettersson,et al.  Stability and robustness for hybrid systems , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

[10]  R. Decarlo,et al.  Asymptotic Stability of m-Switched Systems using Lyapunov-Like Functions , 1991, 1991 American Control Conference.

[11]  Shuzhi Sam Ge,et al.  Controllability and reachability criteria for switched linear systems , 2002, Autom..

[12]  Chi-Tsong Chen,et al.  Linear System Theory and Design , 1995 .

[13]  Cheong Boon Soh,et al.  Lyapunov stability of a class of hybrid dynamic systems , 2000, Autom..

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

[15]  A. Haddad,et al.  On the Controllability and Observability of Hybrid Systems , 1988, 1988 American Control Conference.

[16]  Raymond A. DeCarlo,et al.  Switched Controller Synthesis for the Quadratic Stabilisation of a Pair of Unstable Linear Systems , 1998, Eur. J. Control.

[17]  Thomas Kailath,et al.  Linear Systems , 1980 .

[18]  M. Branicky.  Multiple Lyapunov functions and other analysis tools for switched and hybrid systems , 1998, IEEE Trans. Autom. Control..

[19]  A. Morse,et al.  A cyclic switching strategy for parameter-adaptive control , 1994, IEEE Trans. Autom. Control..

[20]  A. Michel,et al.  Robust stabilizing control laws for a class of second-order switched systems , 1999, Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251).

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

[22]  Zhendong Sun,et al.  On reachability and stabilization of switched linear systems , 2001, IEEE Trans. Autom. Control..

[23]  K. Narendra,et al.  On the stability and existence of common Lyapunov functions for stable linear switching systems , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

[24]  A. Morse,et al.  Stability of switched systems with average dwell-time , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).