Study On Robust Nonfragile Guaranteed Cost H_∞ Control For Switched Singular Systems

Switched system is a special kind of hybrid system, which is composed several subsystems and switching rule that determines the worked subsystem at any time, so that the system is stable. Switched system has a very important theoretical research value and the background of engineering application. Therefore, the study of the stability of the switched system has been attracted more and more attention. On the other hand, with the rapid development of science and technology, the modern control system tends to more complex and large-scale. People found that switched system is easier to describe the dynamic process than other systems, so switched system has been attracted more and more reporters, for example switched singular system, robust H? control for switched system, robust H? guaranteed cost control and so on. The characteristic(uncertain, time-delay, time-varying, parameters perturbation) can reduce performance index, and even can influence the stability of the system. How to make the characteristic uncer control of reasonable range and to reduce the system conservative became a hot and difficult problem in control field.In this paper robust H? control, robust non-fragile H? control for switched system and robust H? guaranteed cost control are investigated.In chapter two, the robust H? control for uncertain switched nonlinear singular systems via LMI approach is concerned. LMI optimization approach and Lyapunov function are used to solve the robust H? control problem. A sufficient condition for the existence of the controller is presented. Finally, a numerical example is provided to demonstrate the effectiveness of the mentioned techniques.In chapter three, the robust non-fragile H? control for non-linear uncertain switched singular time-delay system is mainly studied. The purpose is to contrive a non-fragile controller. It is fragile of the controller themselves that the stability of the system will be descend. So we hope the conreoller is non-fragile, in order to ensure the stability of the system. Based on LMIs, congruent transformation, variable transformation and schur complement, so we can obtain the solves easily. Finally, an example is given, in order to explain the advantage of the result.In chapter four, the problem of robust H? guaranteed cost control for non-linear uncertain switched singular system with multiple time-delay is investigated. The aim is to design a state feedback controller, so that the clsed-loop system is asymptotically stable at zero and the corresponding performance candidate is not more than a given bound. Based on Lyapunov function and the linear matrix inequalities(LMI), a suitable stabilization condition of closed-loop system and explicit expressions of guaranteed cost control are gained. Finally, the results are validated and advantage, throgh a given example.