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

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.