Finite-time stability analysis of impulsive discrete-time switched systems with nonlinear perturbation

Abstract

The problem of finite-time stability for a class of discrete-time switched systems in the presence of both non-Lipschitz perturbation and impulse effects is studied in this paper. Based on the average dwell-time approach, a criterion is proposed which ensures that the system’s state trajectory remains in a bounded region of the state space over a pre-specified finite-time interval if we impose a bound on the initial condition. It is shown that the finite-time stability degree could be greater than one, which is quite different from the existing results for asymptotic stability. Moreover, the total activation time of the Schur stable subsystems does not need to be greater than that of the unstable subsystems. A numerical example is presented to illustrate the effectiveness of the proposed design method.

Keywords:

• discrete-time switched systems
• nonlinear perturbation
• impulsive effect
• finite-time stability

Acknowledgements

The authors would like to thank the associate editor and all the reviewers for their constructive suggestions.

Additional information

Funding

This work was supported by HKU CRCG [grant number 201211159112]; ‘973 Project’ [grant number 2012CB720202]; the National Natural Science Foundation of China [grant number 60774039, [grant number 60974024], [grant number 61074089], [grant number 61174129], [grant number 61374075]; Program for New Century Excellent Talents in University; the Independent Innovation Foundation of Tianjin University.