A numerical technique for the stability analysis of linear switched systems

Abstract

In this paper the ray-gridding approach, a new numerical technique for the stability analysis of linear switched systems is presented. It is based on uniform partitions of the state-space in terms of ray directions which allow refinable families of polytopes of adjustable complexity to be examined for invariance. In this framework the existence of a polyhedral Lyapunov function that is common to a family of asymptotically stable subsystems can be checked efficiently via simple iterative algorithms. The technique can be used to prove the stability of switched linear systems, classes of linear time-varying systems and linear differential lnclusions. We also present preliminary results on another related problem; namely, the construction of multiple polyhedral Lyapunov functions for the specification of stabilizing switching sequences for a switched system constructed from a family of stable linear subsystems.

Acknowledgements

This work was supported by Science Foundation Ireland grant 00/PI.1/C067 and by the European Union funded research training network Multi-Agent Control, HPRN-CT-1999-00107 (This work is the sole responsibility of the authors and does not reflect the European Union's opinion.). Neither the European Union or Enterprise Ireland is responsible for any use of data appearing in this publication. The authors are also grateful to the anonymous reviewers for their constructive comments.