Stability analysis of periodically switched linear systems using Floquet theory

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.