Feedback Stabilization Of A Class Of Discrete-time Linear Switched Systems

Switched linear system is a commonly used hybrid system, which consists ofseveral subsystems, every subsystem is linear, and they are ruled by a switching lawwhich determines how the switching among them works. The stability of switchedlinear systems is a challenging problem because of its varying structure. Thestability lies on not only the stability of sub-systems, but also the switchingsequences. In a result, most of the scholars are concerned about the stability of theswitched systems. Recent years, the research of the switched systems develops fast,many methods are proposed，such as Lyapunov functions, linear matrix inequalities.The main focus of this paper is on researching the feedback stabilization ofdiscrete-time switched systems, judging whether the common Lyapunov functionexists by finding the feedback matrixes.The paper works on the feedback stabilization of a class of discrete-time linearsystems(System VSR-DTSS).First, based on Lie-algebra solvability, the feedbackstabilization of System VSR-DTSS is researched, by translation, we need only applycontrol to the unstable part of the system, that is to say, the reduced system impliesthe stabilization of System VSR-DTSS. Second, based on iterative approximateeigenvector, the feedback stabilization of System VSR-DTSS which doesn’t satisfyLie-algebra condition is researched, by an algorithm via iterative approximateeigenvector, approximate feedback matrix can be found to be stabilized, whichstabilize System VSR-DTSS. In the end, we summarize the content of the thesis andsome weak places are pointed.