Reliability Of A Class Of Switched Linear Systems With Control

By a switched system, we mean a hybrid dynamical system that is composed of a family of continuous-time or discrete-time subsystems and a rule orchestrating the switching between the subsystems. Switched systems as special hybrid systems can provide theoretical methods and practical support for studying hybrid systems. On the other hand, systems in practice have some disturbances and parameters uncertainties because of model errors, measure errors and approximate linearization. Therefore, it is of great signification in both engineering applications and theoretical development to study robust control of uncertain switched systems. In additions, in practical applications, we often encounter some actuator failures or sensor failures. They bring reliable and fault-tolerant demands for control systems. Control systems are required to keep stability where actuator failures or sensor failures occur.In this thesis, we mainly deal with robust reliable control of uncertain switched systems. The contents of this papier are the followings:(1)The problem of H_∞reliable robust state feedback stabilization for switched linear systems whose state and output matrixes with uncertainties is researched. By using the common Lyapunov function method, single Lyapunov function method and multiple Lyapunov function method, a sufficient condition of robust stabilization for switched systems is obtained. Based on LMIs method, robust state feedback controllers and a switching law is designed .They can not only make the closed-loop system quadratic stable but also make it has H_∞performance.(2)We discussed robust guaranteed cost reliable control of switched systems with structural parameters uncertainties. Firstly by means of common Lyapunov function method and designing switched controller, we can not only make the closed-loop system quadratic stable but also make it has cost sector, for all admissible uncertainties and actuator failures occurred in a given failure set under any switching. Secondly, by means of multiple Lyapunov function method, a sufficient condition of robust guaranteed cost quadratic stabilization for switched systems that it exit actuators "serious failure"(the never failed actuators can stabilize the given system) is obtained.(3)The problem of robust reliable control for uncertain linear systems with disturbance is considered. When actuators suffer "serious failure" (the never failed actuators can stabilize the given system) in the system ,none of the controllers can make the system stable. Based on multiple Lyapunov function method, a sufficient condition for the existence of robust controller is obtained by means of multiple controllers switching, which make the loosed-loop system asymptotically stable.