Dissipativity-based asynchronous control of discrete-time Markov jump systems with mixed time delays

This paper addresses the problem of dissipativity-based asynchronous control for a class of discrete-time Markov jump systems. A unified framework to design a controller for discrete-time Markov jump systems with mixed time delays is proposed, which is fairly general and can be reduced to a synchronous controller or a mode-independent controller. Based on a stochastic Lyapunov function approach, which fully utilizes available information of the system mode and the controller, a sufficient condition is established to ensure the stochastic stability and strictly (Q,S,R) dissipative performance of the resulting closed-loop system. Finally, the effectiveness and validity of the proposed method are illustrated with a simulation example.