Asynchronous H_∞Control And Filtering For Discrete-Time Switched Systems

A switched system is one of the most important classes of hybrid systems in engineering applications. It consists of a family of subsystems operated by a particular type of switching rule. Due to the theoretical development as well as practical applications, analysis and synthesis of switched systems have recently gained considerable attention. While, considering the H∞controll or filtering problem, a very common assumption is that the controller or filter is switched synchronously with subsystems, which is quite unpractical. In this thesis, sufficient conditions of the desired filter or controller of discrete time switched systems are derived in term of average dwell time, dwell time and event-driven strategy. The main results obtained in this thesis are as follows:The H∞filtering problem of discrete-time switched delay systems is investigated. Attention is focused on the design of a mean-square exponentially stable filter taking asynchronous switching and missing measurements into account. New results on exponential mean-square stability and a weighted/2-gain analysis for filtering error system are given, where the system is allowed to be unstable during the unmatched interval.For a class of switched systems, a dwell time strategy dependent on the system state is proposed. This switching strategy not only makes the asynchronous H∞state-feedback switched systems stable but also shortens the active time. A new result on stability and l2-gain analysis for switched systems is given. In addition, the restriction of μ times among the Lyapunov function matrices is removed.The asynchronous H∞control problem of discrete-time switched systems is dealt with by state-derived method with dwell time. During the dwell time, the Lyapunov function matrix P(k) varies linearly and becomes invariant afterwards. Switching signals are designed such that the Lyapunov function is decreased at the switching instants, to compensate the possible increment yielded by the asynchronous phenomenon between the system modes and controllers.Finally, draw a conclusion of the results of the thesis and point out some problems which need future study.