Stability analysis of switched systems under dynamical dwell time control approach

Abstract

This article investigates the stability of a class of switched systems using dynamical dwell time approach. First, the condition for stability of switched systems whose subsystems are stable are presented with dynamical dwell time approach, which is shown to be less conservative in switching law design than dwell time approach. Then the proposed approach is extended to the switched systems with both stable and unstable subsystems. Finally, some numerical examples are given to illustrate the effectiveness of the proposed results.

Keywords:

• switched systems
• dynamical dwell time
• switching law
• stability

Acknowledgements

The authors are very grateful to the reviewers and the editors for their helpful comments and suggestions on this article. This work was supported by the Natural Science Foundation of Jiangsu Province (BK2007210) and Sichuan ministry of education scientific research project under Grant 07Zd1123.

Notes

Note

1. Note the k-th switching instant for the switched system equals the k ⁺-th switching instant for subsystems in I+, i.e. t _k + = t _k , therefore t _k + 1 denotes the next instant after t _k + switching to either a stable or unstable subsystem.