Control And Filter For Stochastic Nonlinear Markov Jump Systems With Time-Delay

Markov jump systems are a class of special stochastic hybrid systems,which are widely used in many practical systems such as information and communication engineering,applied economics,aerospace and so on.Some results about Markov jump systems have been obtained,for example controllability and observability,stability analysis,filter design and so on.However,when the parameters of Markov processes take values in an infinite state space,such systems are more suitable for describing many jump phenomena in real systems.At present,the theory of infinite Markov jump system is not mature enough,especially in stability analysis,robust control and filter design.In this paper,robust control and filtering for a class of stochastic nonlinear Markov jump systems with time delays have been studied.The details are given as follows:1.The problem of H? control for stochastic nonlinear infinite Markov jump systems with time delay is studied.Based on Ito's formula and completing the square,the sufficient condition for the existence of infinite horizon asymptotic mean square H? controllers is given by solving a set of coupled Hamilton-Jacobi inequalities(HJIs).Finally,a numerical example and its simulation images are given to illustrate the effectiveness of the results.2.The filtering problem for stochastic nonlinear infinite Markov jump systems with time delay is further studied.Firstly,the nonlinear stochastic bounded real lemma for stochastic nonlinear infinite Markov jumping systems with time delay is offered.The corresponding augmented systems are obtained after the filtering equation constructed.Furthermore,the design method of exponential mean square and asymptotic mean square filter are given by using nonlinear stochastic bounded real lemma.Secondly,the suboptimal H2/H? filter is designed by minimizing the total estimation error energy when the worst-case disturbance is considered.Finally,the effectiveness of the design method is verified by a simulation example.3.Considering the system affected by impulses,the robust fuzzy control problem for stochastic nonlinear impulsive time-delay systems with Markov jump is studied.Firstly,based on global linearization and T-S fuzzy model,the nonlinear systems are linearized by designing appropriate fuzzy rules.Secondly,based on the idea of parallel distributed compensation(PDC)and fuzzy compensation rules,the state equation of the whole fuzzy system are obtained,and the sufficient condition for the stabilization of the fuzzy system is given by linear matrix inequalities(LMIs).Then an exponential stable state feedback fuzzy controller is designed.Finally,numerical and simulation examples are given to verify the correctness of the design method.