A dynamic event-triggered H_∞ control for singular Markov jump systems with redundant channels

ABSTRACT

In this paper, the problem of asynchronous $H_{\mathrm{\infty }}$ control for singular Markov jump systems with redundant channels under the dynamic event-triggered scheme is studied. To save the resource of bandwidth limited network, a dynamic event-triggered scheme is proposed. The technique of redundant channels is employed to improve the successful rate of the communication network, which are modelled as two mutually independent Bernoulli-distributed random variables. A hidden Markov model is proposed to formulate the asynchronisation phenomena between the system modes and the controller modes, which results in the fact that the closed-loop system is a singular hidden Markov jump system. The criteria of regular, causal and stochastically stable with a certain $H_{\mathrm{\infty }}$ performance for the closed-loop system are obtained. The co-design of asynchronous controllers and the dynamic event-triggered scheme is proposed in terms of a group of feasible linear matrix inequalities. A numerical example and a practical example are presented to show the effectiveness of the developed method.

Keywords:

• Dynamic event-triggered scheme
• singular Markov jump systems
• hidden Markov models
• redundant channels
• linear matrix inequalities

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was partly supported by the National Natural Science Foundation of China [grant numbers 61773191, 61803241]; Support Plan for Outstanding Youth Innovation Team in Shandong Higher Education Institutions [grant number 2019KJI010]; Talent Introduction and Cultivation Plan for Outstanding Youth Innovation Team in Shandong Higher Education Institutions.

Notes on contributors

Yanqian Wang

Yanqian Wang received the B.S. degree in automation from Dalian Jiaotong University, Dalian, China, in 2002, and M.S. degree in control theory & control engineering from Shaanxi University of Science and Technology, Xian, China, in 2005, and Ph.D. degree in control science and engineering from Nanjing University of Science and Technology, Nanjing, China, in 2015. He worked as a postdoctoral fellow at University of South Florida from 2015–2016. His research interests include robust control and filtering, singular systems, stochastic systems, networked control systems.

Guangming Zhuang

Guangming Zhuang received his B.S. degree in Mathematics and Applied Mathematics from Liaocheng University, Liaocheng, China, in 2001, M.S. degree in Probability and Mathematical Statistics from South-west University, Chongqing, China, in 2007 and Ph.D. degree in Control Theory and Control Engineering from Nanjing University of Science and Technology in 2016. Since July, 2007, he has been with School of 2 Mathematical Sciences, Liaocheng University, Liaocheng, China. He is currently an Associate Professor of School of Mathematical Sciences, Liaocheng University. His current research interests include robust control and filtering, time delay systems, stochastic systems and singular systems.

Fu Chen

Fu Chen received his B.S. degree in Mathematics and application Mathematics from Taiyuan normal university, Taiyuan, China in 2007, M.S. degree in operational research and cybernetics from Guangxi university, Nanning, China in 2010 and Ph.D. degree in Control Theory and Control Engineering from Nanjing University of Science and Technology in 2014. Since June, 2014, he has been with School of Mathematics and Computer Science, Shanxi Datong University, Datong, China. He is currently a lecturer of School of Mathematics and Computer Science, Shanxi Datong University. His current research interests include quadratic systems, time delay systems, stochastic systems and impulsive systems.