Research On Robust Control For Markov Jump Systems With Partly Known Transition Probabilities

Markov jump system (MJS) is a special kind of stochastic switching system with multiple modes, in which the switches between different modes obey Markov process. For the actual systems with random changing structure or parameters, MJS has strong modeling capabilities. In recent years, Markov jump system has been concerned widely, and the research results are applied in many fields, such as manufacturing systems, flight control, power systems and even economic systems.Initially, the transition probabilities are assumed to be completely known in the studies on Markov jump systems. However, as the result of the limitation of actual conditions, some elements of the transition probability matrix can’t be obtained accurately. Therefore, considerable attention has been paid to Markov jump system with partly known transition probabilities, which are usually divided into completely known and completely unknown cases. In fact, the transition probabilities are obtained from the online or offline measurement, which often have uncertainty. It means a certain range of some unknown transition probabilities can be determined. This bounded information of the unknown probability can’t be used in the framework of the partly known transition probabilities with only two cases. By means of linear matrix inequality (LMI), this thesis concerns the robust control problems of Markov jump systems with more general transition probabilities, which cover the cases that the transition probabilities are exactly known, completely unknown, and unknown but with known bounds. The main contents of this thesis are given as follows:Chapters 1-2 first summarize and analyze the basic conceptions and development of Markov jump system. Then preliminaries about the considered problem are also given.In the Chapter 3, the existing stability conditions for Markov jump linear systems (MJLSs) are improved. Based on the improved results, the H2 and H∞ controller design conditions for MJLSs are presented. The simulation results show that the proposed method is less conservative.Chapter 4 investigates robust control problems for Markov jump systems with parameter uncertainty. Based on the parameter-dependent Lyapunov function, the less conservative stabilization condition is presented. The effectiveness of the method is verified through simulation.Chapter 5 is concerned with the stability problem of a kind of time-delay Markov jump nonlinear systems. A new Lyapunov-Krasovskii functional is constructed to derive a less conservative delay-dependent stability condition, and the simulation results are presented.Finally, the results of the dissertation are summarized and further research topics are pointed out.