Average Dwell-time Method to Stabilization and L2-gain Analysis for Uncertain Switched Nonlinear Systems

Abstract This paper is concerned with the problem of stabilization and L 2 -gain analysis for a class of switched nonlinear systems with norm-bounded time-varying uncertainties. A system in this class is composed of two parts: a uncertain linear switched part and a nonlinear part, which are also switched systems. When all the subsystem are stabilizable and have a L 2 -gain, the switched feedback control law and the switching law are designed respectively using average dwell-time method such that the corresponding closed-loop switched system is exponentially stable and achieves a weighted L 2 -gain. We construct the Piecewise Lyapunov functions and design the switching law based on the structural characteristics of the switched system.

[1]  P. Khargonekar,et al.  Robust stabilization of uncertain linear systems: quadratic stabilizability and H/sup infinity / control theory , 1990 .

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

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

[4]  Bo Hu,et al.  Disturbance attenuation properties of time-controlled switched systems , 2001, J. Frankl. Inst..

[5]  S. Pettersson,et al.  Stabilization of hybrid systems using a min-projection strategy , 2001, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).

[6]  Jun Zhao,et al.  Stability and L2-gain analysis for switched delay systems: A delay-dependent method , 2006, Autom..

[7]  Bo Hu,et al.  Stability analysis of switched systems with stable and unstable subsystems: An average dwell time approach , 2001, Int. J. Syst. Sci..

[8]  Daizhan Cheng,et al.  Stabilization of planar switched systems , 2004, Syst. Control. Lett..

[9]  Stefan Pettersson,et al.  Analysis and Design of Hybrid Systems , 1999 .

[10]  Wang Ren-ming.  Stability analysis for a class of nonlinear switched systems , 2004 .

[11]  G. Zhai.  Quadratic stabilizability of discrete-time switched systems via state and output feedback , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[12]  M. Zaremba,et al.  Quadratic stability of a class of switched nonlinear systems , 2004, IEEE Transactions on Automatic Control.

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

[14]  Daizhan Cheng,et al.  On quadratic Lyapunov functions , 2003, IEEE Trans. Autom. Control..

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

[16]  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).

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

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

[19]  I. Petersen.  A stabilization algorithm for a class of uncertain linear systems , 1987 .