Dissipative Control For Markov Jump Systems With Partly Unknown Transition Probabilities

Transition probabilities in the Markov jump systems are key parameters,many scholars have studied the systems under the assumption that the transition probabilities are known.In actual engineering,it is very difficult to obtain the full transition probabilities information accurately,so the study of the Markov jump systems whose transition probabilities are partly unknown,becomes necessary.In this paper,the dissipative control problem of Markov jump systems with partly unknown transition probabilities is studied.Firstly,we outline not only the prospects of Markov jump systems and time-delay systems but the current status of research for MJSs all over the world.Secondly,the stochastic stability,passive and dissipative problems of time-delay Markov jump systems with partly unknown transition probabilities are studied respectively,then we get sufficient conditions for stochastic stability,passive and dissipative control of the systems;We discuss the stability of the systems by selecting the appropriate Lyapunov function and adding the free power zero matrix appropriately;Then the state feedback controllers are designed,we use the linear matrix inequality method to obtain sufficient conditions of the passive and dissipative control for the systems,and the feasibility of the conclusion is verified by the numerical examples;Finally,we summarize the full paper.