Practical stability and stabilization of hybrid and switched systems

In this note, practical stability and stabilization problems for hybrid and switched systems are studied. The main results of this note include a direct method for the /spl epsi/-practical stability analysis of hybrid systems and sufficient conditions for the practical stabilizability of switched systems. We construct an /spl epsi/-practically stabilizing switching law in the proof of the practical stabilizability result and apply it to a tracking problem to show its effectiveness.

[1]  A. Michel,et al.  Generalized practical stability analysis of discontinuous dynamical systems , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

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

[3]  P. Dorato,et al.  Finite time stability under perturbing forces and on product spaces , 1967, IEEE Transactions on Automatic Control.

[4]  V. Lakshmikantham,et al.  Practical Stability Of Nonlinear Systems , 1990 .

[5]  J. H. Leet,et al.  Worst-case formulations of model predictive control for systems with bounded parameters , 1997, Autom..

[6]  Jos F. Sturm,et al.  A Matlab toolbox for optimization over symmetric cones , 1999 .

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

[8]  A. Michel,et al.  Analysis of discontinuous large-scale systems: stability, transient behaviour and trajectory bounds , 1971 .

[9]  Basil Kouvaritakis,et al.  Efficient robust predictive control , 2000, IEEE Trans. Autom. Control..

[10]  Xuping Xu.  Practical stabilizability of a class of switched systems , 2004, Proceedings of the 2004 American Control Conference.

[11]  Guisheng Zhai,et al.  On Practical Stability and Stabilization of Hybrid and Switched Systems , 2004, HSCC.

[12]  A. Michel.  Quantitative analysis of simple and interconnected systems: Stability, boundedness, and trajectory behavior , 1970 .

[13]  C. Scherer,et al.  Multiobjective output-feedback control via LMI optimization , 1997, IEEE Trans. Autom. Control..

[14]  Joao P. Hespanha,et al.  Logic-based switching algorithms in control , 1998 .

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

[16]  Panos J. Antsaklis,et al.  Practical stabilization of integrator switched systems , 2003, Proceedings of the 2003 American Control Conference, 2003..

[17]  Guisheng Zhai,et al.  On practical stability of switched systems , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

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

[19]  R. Decarlo,et al.  Perspectives and results on the stability and stabilizability of hybrid systems , 2000, Proceedings of the IEEE.

[20]  P. Hartman.  Ordinary Differential Equations , 1965 .