Event-Triggered Multiasynchronous H∞ Control for Markov Jump Systems With Transmission Delay

In this article, the issue of event-triggered multiasynchronous
$H_{\infty }$
control for Markov jump systems with transmission delay is concerned. In order to reduce sampling frequency, multiple event-triggered schemes (ETSs) are introduced. Then hidden Markov model (HMM) is employed to describe multiasynchronous jumps among subsystems, ETSs, and controller. Based on the HMM, the time-delay closed-loop model is constructed. In particular, when triggered data are transmitted over networks, a large transmission delay may cause disorder of transmission data such that the time-delay closed-loop model cannot be developed directly. To overcome this difficulty, a packet loss schedule is presented and the unified time-delay closed-loop system is obtained. By the use of the Lyapunov–Krasovskii functional method, sufficient conditions with the controller design are formulated for guaranteeing the
$H_{\infty }$
performance of the time-delay closed-loop system. Finally, the effectiveness of the proposed control strategy is demonstrated by two numerical examples.