Robust finite-time H^∞ control of switched systems and its applications: a dynamic event-triggered method

Abstract

This paper considers the problem of finite-time $H_{\mathrm{\infty }}$ control for switched systems under a dynamic event-triggered mechanism. In order to avoid frequent switching phenomenon and exclude Zeno behavior, discrete state information is used to construct a state-dependent switching law and a dynamic event-triggered mechanism. The event-triggered condition only needs to be detected at the sampled instants, so the data transmission pressure is greatly relieved. By introducing a delay-dependent Lyapunov function with the internal dynamic variable, a criterion is established to achieve the finite-time $H_{\mathrm{\infty }}$ performance. A set of dynamic event-triggered controllers and a state-dependent switching law are co-designed to reach desired behavior. An application example of the switched RLC system is offered to demonstrate the advantages of the acquired method.

Keywords:

• Dynamic event-triggered mechanism
• finite-time boundedness
• $H_{\mathrm{\infty }}$ performance
• switched systems
• state-dependent switching

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was partially supported by the National Natural Science Foundation of China under Grant Number [61773235], partially by Postgraduate Tutor Guidance Ability Improvement Project of Shandong Province under Grant Number [SDYY18125], partially by Consulting Project of China Academy of Engineering [2021XY39], and partially by the Taishan Scholar Project of Shandong Province under Grant Number [TSQN20161033].

Notes on contributors

Guangdeng Zong

Guangdeng Zong received the M.S. degree in Mathematics from Qufu Normal University, Qufu, China, in 2002, and the Ph.D. degree in Control Theory and Control Engineering from the School of Automation, Southeast University, Nanjing, China, in 2005. He is a Full Professor with Qufu Normal University, Rizhao, China. He is currently an Editorial Board Member for some international journals, such as International Journal of Systems Sciences. His current research interests include robust control and switched systems.

Xue Sun

Xue Sun received the B.S. degree in mathematics from Liaocheng University, Liaocheng, China, in 2019. She is currently working towards her master's degree in Qufu Normal University of China, Rizhao. Her key research topics are switched systems, finite-time control and event-triggered control.

Dong Yang

Dong Yang received the M.S. degree in mathematics from Qufu Normal University, Qufu, China, in 2010, and the Ph.D. degree in control theory and control engineering from College of Information Science and Engineering, Northeastern University, Shenyang, China, in 2017. He is currently an Associate Professor with Qufu Normal University, Rizhao, China. His research interests include switched LPV systems, switched systems, $H_{\mathrm{\infty }}$ control and their applications.

Mohammed Chadli

Mohammed Chadli received his PhD thesis in Automatic Control from the University of Lorraine (UL), CRAN-Nancy in 2002. He is currently Full Professor at the University Paris-Saclay, Univ Evry, IBISC Lab., France. His research interests include filtering and control problems and applications to vehicle systems, intelligence systems, network systems and cyber-physical systems. He is in the editorial board of several international journals, such as IEEE Transactions on Fuzzy Systems, Automatica.

Kaibo Shi

Kaibo Shi received Ph.D. degree in School of Automation Engineering at the University of Electronic Science and Technology of China. He is a professor of School of Information Sciences and Engineering, Chengdu University. His current research interests include stability theorem, robust control, sampled-data control systems, networked control systems and neural networks. He is the author or coauthor of over 60 research articles. He is a very active reviewer for many international journals.