Mathematical Problems in Engineering
Volume 2004 (2004), Issue 1, Pages 1-10
doi:10.1155/S1024123X04401069

Stability analysis of periodically switched linear systems using Floquet theory

Cevat Gökçek

Department of Mechanical Engineering, Michigan State University, East Lansing 48824, MI, USA

Received 23 January 2004; Revised 6 February 2004

Copyright © 2004 Cevat Gökçek. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Stability of a switched system that consists of a set of linear time invariant subsystems and a periodic switching rule is investigated. Based on the Floquet theory, necessary and sufficient conditions are given for exponential stability. It is shown that there exists a slow switching rule that achieves exponential stability if at least one of these subsystems is asymptotically stable. It is also shown that there exists a fast switching rule that achieves exponential stability if the average of these subsystems is asymptotically stable. The results are illustrated by examples.