Asynchronous Observer-Based Control for Exponential Stabilization of Markov Jump Systems

This brief investigates the problem of asynchronous observer-based control for a class of discrete-time Markov jump systems (MJSs). Compared with most existing results on observer-based control of MJSs, the proposed asynchronous observer-based controller has its own jump mode thus not necessarily to work synchronously with the controlled systems. Based on stochastic Lyapunov function approach, sufficient criteria are derived to ensure the exponential stability with a predefined $H_{\infty }$ performance of the resulting closed-loop system. Moreover, to determine gains of the observer-based controller, two totally different linearization methods are presented and the later one is proved to be less conservative. A numerical example is provided to illustrate the effectiveness of the proposed design techniques.