Asynchronous Control for Positive Markov Jump Systems

A new result is provided for the asynchronous control analysis of positive Markov jump systems (PMJSs) in this paper. Firstly, a hidden Markov model is described to express the asynchronous circumstances that appear between the system modes and controller modes. Secondly, by utilizing a copositive stochastic Lyapunov function, a sufficient and necessary condition is given to guarantee the mean stability of PMJSs. Thirdly, we obtain another equivalent condition and design the corresponding asynchronous controller. Finally, the correctness of these results is verified by two numerical examples.