New results on practical stabilization and practical reachability of switched systems

The present paper has two main contributions. First, we report new sufficient conditions for practical stabilizability of switched systems. Such conditions are geometrically more appealing and easier to check than conditions proposed in our previous papers. The conditions are applicable to practical stabilizability problems over infinite or finite time intervals. Second, we study the practical reachability problems in the light of our practical stabilization results. Sufficient conditions for practical reachability are presented.

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

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

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

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

[5]  Solomon Lefschetz,et al.  Stability by Liapunov's Direct Method With Applications , 1962 .

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

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

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

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

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

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

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

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

[14]  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).

[15]  T. Apostol.  Mathematical Analysis , 1957 .