Stability analysis of periodically switched linear systems using Floquet theory

摘要

Stability of a switched system that consists of a set of lineartime invariant subsystems and a periodic switching rule isinvestigated. Based on the Floquet theory, necessary andsufficient conditions are given for exponential stability. It isshown that there exists a slow switching rule that achievesexponential stability if at least one of these subsystems isasymptotically stable. It is also shown that there exists a fastswitching rule that achieves exponential stability if the averageof these subsystems is asymptotically stable. The results areillustrated by examples.