The Design Of The State Observer For Switched Linear Singular Systems

Dynamical systems that are described by an interaction between continuous anddiscrete dynamics are usually called hybrid systems. Switched systems are a class ofimportant hybrid systems. In fact, singular system is a kind of dynamical systemswhich is used more extensive than normal systems, thus, the research for switchedsingular systems is more universal.The state feedback is used when the state is not directly available in switchedsingular systems. Base on the singular systems, switched systems theory and theexisting stability results of switched singular systems, the state observer for switchedlinear singular systems is studied in this paper. This paper is summarized as follows:Firstly, a brief overview of singular systems, switched systems and switchedsingular systems is given, and the basic knowledge of we used is given. At the sametime, state observer of singular systems and switched systems are introduced.Secondly, the state observer existing problems of two kinds of switched singularsystems are discussed. Using common Lyapunov, and the necessary condition isgiven for the state observer of switched linear singular systems under arbitraryswitching sequence. Using convex combination technique, and the necessarycondition is given for the state observer of switched linear singular systems when allsubsystems are unobservable. And give numerical examples.Finally, the conclusions and problems for future research are given.