Stability And Stabilization Problems Of The Linear Peroidic Switched Systems

The hybrid system is a class of a complex systems, it is composed by conti-nous dynamic and discrete dynamic which effect each other. Recently, it becomes the one hotspot issues of control field. As an important and familiar hybrid system, the switched system gains the more extentive application with the rapid development of the computer technique.In this paper, the exponential stability and stabilization of linear switched system under certain assumptions are mainly studied. Based on the Floquet theory, sufficient conditions are given for stabilization. Then it is showed that there exists a slow switching rule and fast switching rule that stabilize the periodically switched linear time-invariant systems under certain conditions. At last, necessary and sufficient conditions are given for exponential stability if the periodic time-varying system satifles certain conditions. It provides sufficient conditions of static output feedback stabilization for periodically switched linear time-varying systems according to a new linear matrix inquality which is constrainted to a slack variable condition.