Observer-based Robust Stabilization For A Class Of Switched Systems

As a kind of important hybrid system, switched systems have important theoryvalue and broad application background. The research problem of the switchedsystem with uncertainty is mainly studied by designing the controller that makes thesystem realize robust stabilization. The uncertain model mainly involves linearuncertain model, convex polytopic uncertain model, bounded uncertain model,dependence model on affine parameters, and so on. Besides, the design of thecontroller is mostly dependent on the state of the system. The research problems ofthe switched systems are mainly concerned with stability and controller design,which have made many achievements. However, the states for many practicalswitched system are uncertain or cannot be completely measurable. Therefore, fromthe point of view of the observer, the robst stabilization problems in this paper willbe reconsidered for the switched linear systems and nonlinear switched systems. Theuncertain matching conditions and the form of what we need are all obtained through“rank1” decomposition. This paper is divided into five parts:The thesis begins with the concept of switched systems and its development,and then the concept of the observer and the research status and situation of theswitched systems observation are introduced.The second part of the thesis will be mainly devoted to studying a kind ofautonomous and uncertain switched linear systems based on the stability problem ofthe observer. By using the method of common Lyapunov function and multipleLyapunov function, the author has given the sufficient condition of the asymptoticstability of the augmented system, so as to get the sufficient conditions of systemstability based on the observer.In the third part, a kind of autonomous and uncertain switched linear systemsbased on the feedback stabilization problem of the observer will be mainlyresearched. Designing the switching law and control law of the systems, this chaptermainly uses the method of multiple Lyapunov function and Schur complementlemma, in order to obtain the sufficient conditions of the non-autonomous switched linear systems based on the robust stabilization problem of the observer.The fourth part of the thesis is based on the stabilization problem of theobserver, and the author mainly researches a kind of nonlinear switched systems thathave Lipschitz constraints. Through using multiple Lyapunov function method anddesigning control law and switching law, the author has obtained the sufficientcondition of the nonlinear switched systems based on the stabilization of theobserver.Finally, the author summarizes the whole thesis and makes prospects for thefuture job.