State feedback for networked Markov jump systems with time-delays

This paper investigates the state feedback control problem for networked Markov jump systems with time-delays on condition that the transition probabilities of system modes and time-delays are partly unknown. First, the time-delay from sensor to controller and the time-delay from sensor to actuator are both considered which are described by two independent Markov chains. Furthermore, the closed-loop systems are molded as control systems which contain three Markov chains. Under this framework, the sufficient conditions on stochastically stability of the closed-loop systems are derived in terms of matrix inequalities by constructing Lyapunov-Krasovskii functions. The method of calculating controller gain matrix is also given. Finally, a numerical simulation example is used to show the validity of the proposed method.