Study On Several Problems Of Switched Systems

This dissertation is concerned with some issues related to the analysis and controldesign of switched systems, and main contributions are summarized as follows:1) The model change caused by switching is equivalent to parameter uncertainty for a classof continuous time switched linear systems, and stability and robust stability areinvestigated for the switched systems. The sufficient condition of stability is presentedbased on common quadratic Lyapunov function and the method is used to analyze thestability and robust stability of a class of discrete time switched linear systems, furthermore,the sufficient condition of stability is obtained. The stability of a class of discrete timestate-dependent switched linear system is investigated, the S-Procedure is employed toconsider the state regions, and the sufficient condition of stability for the switched systemsis presented, further, the problem of state feedback stabilization of this class of systems isaddressed.2) The robust stabilization problem of a class of uncertain discrete time switched linearsystems is investigated under arbitrary switching, and the design schemes of state feedbackcontrollers are presented in terms of linear matrix inequality(LMI). Further, the disturbanceattenuation problem for a class of uncertain discrete time switched systems is investigated,the sufficient conditions for the switched systems to be robust stable with H_∞disturbanceattenuation is presented, and the state feedback controllers are designed to improve theperformance of disturbance attenuation for the switched systems.3) The problem of optimal design of sub-controller of continuous time switched linearsystems is addressed. The definition of traditional H_∞norm is extended to the case oflocal frequency range, a new conception of window H_∞norm is presented, andgeneralized bounded real theorem is obtained using GKYP Lemma. An optimal designmethod for PID controller is provided according to approximate model-matching principle,and the problem of PID controller design is converted into window H_∞normoptimization problem. The sufficient and necessary conditions for the existence of the PIDcontroller parameters are presented such that the approximate model-matching problem issolvable, and relevant results are presented for low frequency range, middle frequencyrange and high frequency range. Another PID controller design method is provided basedon magnitude margin and phase margin, and PID controller parameters are obtained bysolving LMI. The method of controller state reset stabilization is investigated to ensurestability of the switched linear systems, and the sufficient and necessary conditions for the existence of the reset mapping are presented, further, the constructive method of resetmapping is provided.4) A design method of stabilization controller for a class of switched affine nonlinearsystems is provided based on Sontag's method. The polynomial function is used as thecommon Lyapunov function of switched polynomial nonlinear systems, and two designmethods of stabilization controller are presented. The first is direct method and feedbackcontrollers can be obtained by solving feasibility problem of sum of square program. Thesecond method is iterative method and feedback controllers can be obtained by solvingoptimization problem of sum of square program. An iterative method to designstabilization controller for a class of state-dependent switched polynomial nonlinearsystems is provided based on piecewise polynomial Lyapunov functions.