Dynamic event-based mixed H∞ and dissipative asynchronous control for Markov jump singularly perturbed systems

Abstract

The paper investigates the issue of mixed H∞ and dissipative asynchronous controller design for a class of Markov jump singularly perturbed systems (MJSPSs). A suitable dynamic event-triggered rule is offered to further mitigate the transmission burden of communication network. Since the mode information of Markov chain is extremely difficult to get, an asynchronous controller is well constructed. Hence, a hidden Markov model (HMM) is chosen to describe the non-synchronous facts between states of the original Markov chain and the constructed non-synchronous controller. Resorting to the Lyapunov functional concerning the internal dynamic variable, sufficient conditions of stochastically stable with a certain mixed H∞ and dissipative performance for the resulting closed-loop MJSPSs are offered. Based on the LMI technique, the design framework of asynchronous controller and the dynamic event-triggered rule are given in a unified way. Lastly, a modified DC motor model is offered to demonstrate the superiority of the proffered method.