Stability And Stabilization For A Class Of Nonlinear Discrete-time Singular Markov Jump Systems With Time-varying Delay

In this paper, research background of singular systems, singular Markov jump systems, and nonlinear Markov jump systems is introduced. The sta-bility, robust stability, state feedback stabilization and static output feedback stabilization problems for a class of nonlinear discrete-time singular Markov jump systems with time-varying delay are discussed.In chapter2, the stability problem for nonlinear discrete-time singular Markov jump systems with time-varying delay is investigated. First, based on stochastic switched Lyapunov functional and implicit function theorem, a linear matrix inequality (LMI)sufficient condition is developed which guar-antees that the nonlinear discrete-time singular Markov jump systems with time-varying delay are regular, causal, have unique solution in a neighborhood of the equilibrium point, and are stochastically stable. Then, in order to fa-cilitate the design of the controller, based on this stability condition, by using a series of matrix inequalities, another sufficient condition for the systems to be regular, causal, have unique solution in a neighborhood of the equilibrium point and be stochastically stable is obtained. Last, a numerical example is given to show the correctness and effectiveness of the proposed methods.In chapter3, the robust stability for nonlinear discrete-time singular Markov jump systems with time-varying delay is discussed. Based on the stability condition of chapter2, by using a series of matrix inequalities to deal with the uncertainties, LMI sufficient condition of robust stability is obtained. A numerical example is given to show the correctness and effectiveness of the proposed methods.In chapter4, the state feedback stabilization and static output feedback stabilization for nonlinear discrete-time singular Markov jump systems with time-varying delay are studied. From the stability condition in chapter2, by using LMI, the existed condition and design method of the state feedback stabilization controllers are obtained. By using singular value decomposition approach and LMI technique, the existed condition and design method of static output feedback controllers are given. Last, a numerical example is given to show the correctness and effectiveness of the proposed methods.