Analysis And Control Of Linear Arbitrarily Switched Systems And MARKOV Stochastically Switched Systems

Switched systems are an important category of hybrid systems, which consist of continuous-time subsystems or discrete-time subsystems and the rule acting among them. Many practical engineering issues can be described by this class of switched systems. Due to the signaficance of both theory and broad practical applications, the study of switched systems has been received much attention, and has become one of the hotspots of research in the field of systems science.A special class of switched systems is the systems with Markovian jump parameters, i.e. Markovian switching systems (or say Markovian jump systems), in which the transitions among differengt regimes are random and are further supposed as a Markov process. Due to the complicated hybrid information structure, the research of this class of jump systems can not be treated as simple combination of traditional control theories for the continous systems driven by time or discrete events systems. Thus, the invetigation of the control theories for Markovian switching systems is a challenging work.Based on Lyapunov stability theory together with linear matrix inequility technique, this dissertation investigates the analysis and synthesis problems for the above-mentioned switched systems, and the main contributions are as follows:(1) The basic conceptions and concerned definitions of switched systems are introduced, then, the internal and overseas research situations for the control theory of switched systems are classified and summarized, where the theoretical significance and the practical application backgrounds are given, and the study objects and contents of this dissertation are presented.(2) The pole placement problem is studied for a class of linear discrete-time switched systems with parameter uncertainties by introducing the conception of robust D - stability. Then a state-feedback controller is designed to make the closed uncertain system be robust D -stable and have H_∞performance.(3) The robust H_∞and l₂-l_∞output feedback controllers via state-reset are designed for a class of uncertain linear discrete-time switched systems. We address output feedback stabilization algorithms through resetting the state of the controllers at the switching moments, in which more optimized H_∞and l₂-l_∞performances are required for the closed systems.(4) The stochastic stability of Markovian switching systems with time-varying delays is investigated. Based on the stochastic stability theory, new stability criteria are obtained in terms of LMIs by constructing different Lyapunov-Krasovskii functional. Then, the H_∞filtering algorithm is proposed.(5) For a class of Markovian switching systems with mode-dependent time-varying delays, the stochastic stability and stabilization problems are concerned. Meanwhile, based on the stochastic bounded real lemma, the condition is derived from the H_∞performance. According to the new H_∞performance criterion, our attention is focused on the H_∞control problem for this class of systems.(6) The stability problem for a class of Ito? stochastic Markovian switching systems with time delays is investigated. By constructing an improved Lyapunov-Krasovskii functional, a tighter upper bound of its derivative is established, and the exponential mean-square stability condition with reduced conservativeness is obtained for this class of systems. Then, the H_∞filter is designed for such class of systems.