Passivity, feedback equivalence and stability of switched nonlinear systems using multiple storage functions

In this paper, we address the issues of passivity, feedback equivalence and stability for switched nonlinear systems via a multiple storage function method. Since the storage function of each subsystem may jump at the switched on time sequences, we present a concept of generalized passivity for switched systems by multiple storage-like functions. Based on this, the conditions for the passivity of switched nonlinear systems is given. Furthermore, the problem of feedback passivation and the passivity-based stability of switched nonlinear systems are investigated.

[1]  Shengwei Mei,et al.  Passivity-based H∞ Control for APF in Three- phase Four-wire Distribution Power Systems , 2006 .

[2]  Jun Zhao,et al.  Dissipativity Theory for Switched Systems , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[3]  Nael H. Ei-Farra,et al.  Output feedback control of switched nonlinear systems using multiple Lyapunov functions , 2001 .

[4]  J. Willems.  Dissipative dynamical systems part I: General theory , 1972 .

[5]  Alberto Bemporad,et al.  Passivity Analysis and Passification of Discrete-Time Hybrid Systems , 2008, IEEE Transactions on Automatic Control.

[6]  Mile J. Stankovski,et al.  Passivity and feedback equivalence of switched nonlinear systems with storage-like functions , 2010, 2010 IEEE International Conference on Systems, Man and Cybernetics.

[7]  João P. Hespanha,et al.  Nonlinear observability notions and stability of switched systems , 2003 .

[8]  M. Jirstrand,et al.  On stability and passivity of a class of hybrid systems , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

[9]  Mark W. Spong,et al.  Passivity-Based Control of Multi-Agent Systems , 2006 .

[10]  Jun Zhao,et al.  Passivity and stability of switched systems: A multiple storage function method , 2008, Syst. Control. Lett..

[11]  Z. Jiang,et al.  Passivity-based control of nonlinear systems: a tutorial , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

[12]  A. Isidori,et al.  Passivity, feedback equivalence, and the global stabilization of minimum phase nonlinear systems , 1991 .

[13]  Mehrdad Saif,et al.  PASSIVITY AND PASSIVITY BASED CONTROLLER DESIGN OF A CLASS OF SWITCHED CONTROL SYSTEMS , 2005 .

[14]  Bernhard Maschke,et al.  Dissipative Systems Analysis and Control , 2000 .

[15]  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).

[16]  F. Allgower,et al.  Passivity-based nonlinear dynamic output feedback design: a semidefinite programming approach , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[17]  P. Moylan,et al.  The stability of nonlinear dissipative systems , 1976 .

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

[19]  Wassim M. Haddad,et al.  Dissipativity theory and stability of feedback interconnections for hybrid dynamical systems , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[20]  Jun Zhao,et al.  On stability, L2-gain and Hinfinity control for switched systems , 2008, Autom..

[21]  Daniel Liberzon,et al.  Nonlinear Systems , 2004 .

[22]  A. Morse,et al.  STABILITY OF SWITCHED SYSTEMS WITH AVERAGE , 1999 .

[23]  Jun Zhao,et al.  Dissipativity Theory for Switched Systems , 2005, CDC 2005.

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

[25]  Bin Jiang,et al.  Fault Tolerance Analysis for Switched Systems Via Global Passivity , 2008, IEEE Transactions on Circuits and Systems II: Express Briefs.

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