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

• Published in: Applied mathematics and computation 2020-12, Vol.386, p.125443, Article 125443
• Main Authors: Wang, Yanqian, Chen, Fu, Zhuang, Guangming, Yang, Guang
• Format: Article
• Language: English
• Subjects: Asynchronous control; Dynamic event-triggered rule; Hidden Markov model; Linear matrix inequality; Markov jump singularly perturbed systems
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2020.125443

•Sufficient conditions of stochastically stable with a certain mixed H∞ and dissipative performance for the resulting closed-loop MJSPSs are obtained.•The existence of non-synchronous controller and the developed event-triggered rule is offered in a unified framework. 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.