Analysis Of Markov Stochastic System With Mixed Time Delays And Uncertain Parameters

Markov stochastic system is one kind of important stochastic systems. It has wideapplications in human beings’ manufacturing and life because of Markov characteristicof system status changes. Study of Markov stochastic systems is of profound theoreticalsignificance and great practical values. It receives especial attentions from experts athome and abroad, and has become one of the hot research issues of current stochasticsystems.In this thesis, we study the stability problem of a typical class of Markov stochasticsystem, which simultaneously possesses time delays, perturbations and uncertainty(certainty) parameters. Because Markov problems are frequently encountered in prac-tical engineering problems, study of such kind of problems has theoretical and appliedimportance. We obtain the following research results by constructing appropriate Lya-punov functional.The asymptotic stability is investigated for Markov jumping functional differentialequations with time delays. By means of constructing the Lyapunov-Krasovskii func-tional and utilizing analysis methods of linear matrix inequalities, the asymptotic stabil-ity condition is presented for the Markov jump systems with time delays. The correct-ness and efficiency of the acquired results are demonstrated by numerical simulations.The mean square exponential stability is studied for Markov stochastic systemswith uncertain parameters. Due to construction of complex Lyapunov-Krasovskii func-tional, introduction of appropriate free weight matrix, combination of matrix inequalityanalytical techniques, we obtain the matrix inequalities for the mean square exponentialstability of the Markov mixed stochastic systems, and generalize our results to stochas-tic systems with time-varying delays and distributed delays as well as to non-perturbedmixed systems.