Static Output Feedback l2 – l∞ Asynchronous Control of Markov Jump Systems Under Dynamic Event-Triggered Scheme

This article studies the control problem of the discrete-time Markov jump systems (MJSs). First, the asynchronous switching between the plant modes and the controller modes is taken into consideration. To handle this issue, the estimated modes are utilized in the controller design. Second, in order to reduce the frequency of data transmission in the control system, a dynamic event-triggered communication scheme is introduced into the controller-to-actuator channel. Third, the exogenous disturbance is considered and the $l_{2}-l_{\infty }$ performance index is introduced. In addition, all the states are unavailable and only the output signals are used for the feedback design. The highlight of this study is that a more general case is considered, in which both the plant modes and the states are assumed to be unavailable. The fundamental issue is to determine the feedback gains and the event-triggering matrix simultaneously such that the closed-loop MJSs are stochastically stabilized with a certain level of $l_{2}-l_{\infty }$ performance. By constructing a mode-dependent Lyapunov function, a set of sufficient conditions is derived and the control algorithm is developed. At last, a numerical example and a DC-DC switched boost converter circuit are given to show the effectiveness and practicability of the proposed control technique.