Research On Feedback Control Of Singular Switched Systems

Switched systems are important class of hybrid systems, which is composedby several subsystems and a switching law that decides the active subsystem ateach instant time. Singular systems, are also called descriptor systems, have moreextensive sense than normal systems. If all of the subsystems are singularsystems, we called them singular switched systems. In many practical systems,there exist uncertainty because of the measuring sensitivity is not enough or thecomponents aging. So we put forward the uncertain singular switched system.Also the system exist the lag phenomenon because of the informationtransmission, computing time and observation delay. So we put forward the time-delay singular switched systems. The study of uncertain singular switched systemand time-delay singular switched system has the vital significance.Based on Lyapunov stability theory and singular systems, using linearmatrix inequalities method, this dissertation mainly investigates the problems ofrobust H control for uncertain singular switched system, time-delay singularswitched systems and a class of uncertain time-delay systems respectively. Themain results obtained in this dissertation are summarized as follows:First, the linear singular switched systems are introduced. The robuststability for a class of uncertain singular switched systems is studied with theresearch methods in stability of switched systems and singular systems. Andcontrol switching rules of the corresponding state feedback controller anddynamic output feedback controller are designed. The sufficient conditions forstability of the systems are given.Then, the state feedback control for a class of singular switched systemswith time-delay is studied. The sufficient conditions of the system state feedbackcalm is described with matrix inequality by the common Lyapunov function andconvex combination technology. The corresponding controller and switchingrules are designed. And convert them to the linear matrix inequality using by variable substitution method.Finally, we analyze robust a class of H stability for a class of uncertainsingular switched systems, which input have time-delay and the input with thestate both have time-delay, respectively. The sufficient conditions of the systemstate feedback calm is described with linear matrix inequality by the commonLyapunov function and convex combination technology. The correspondingcontroller and switching rules are designed to ensure the closed system is statefeedback calm with robust H interference suppression. A numericalexample is given to illustrate the effectiveness of the proposed method.Numerically calculating examples are given to validate the effectiveness ofthe results in every part of the dissertation.