Mathematical Problems in Engineering
Volume 2004 (2004), Issue 1, Pages 1-10
Stability analysis of periodically switched linear systems using Floquet theory
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.
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.