Analysis and Design of Markov Jump Systems with Complex Transition Probabilities (Studies in Systems, Decision and Control #54)

By: Peng Shi and Lixian Zhang and Ting Yang and Yanzheng Zhu

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Synopsis: The bookaddresses the control issues such as stability analysis, control synthesis andfilter design of Markov jump systems with the above three types of TPs, andthus is mainly divided into three parts. Part I studies the Markov jump systemswith partially unknown TPs. Different methodologies with different conservatismfor the basic stability and stabilization problems are developed and compared. Then the problems of state estimation, the control of systems with time-varyingdelays, the case involved with both partially unknown TPs and uncertain TPs ina composite way are also tackled. Part II deals with the Markov jump systemswith piecewise homogeneous TPs. Methodologies that can effectively handlecontrol problems in the scenario are developed, including the one coping withthe asynchronous switching phenomenon between the currently activated systemmode and the controller/filter to be designed. Part III focuses on the Markov jumpsystems with memory TPs. The concept of σ-mean square stability is proposedsuch that the stability problem can be solved via a finite number ofconditions. The systems involved with nonlinear dynamics (described via theTakagi-Sugeno fuzzy model) are also investigated. Numerical and practicalexamples are given to verify the effectiveness of the obtained theoreticalresults. Finally, some perspectives and future works are presented to concludethe book.