Exponential stability and L₂ gain analysis of switched distributed parameter systems with time delay

Abstract

The present paper is concerned with stability and $L_2$ gain analysis of switched distributed parameter system (SDPS) with time delay. First, exponential stability is discussed, and the state decay estimate of the system is explicitly given by using linear matrix inequalities (LMIs) incorporating with the average dwell time (ADT) method. Second, $L_2$ gain analysis is also studied. At last, illustrative examples are given to show the effectiveness of the proposed method. The main contribution of the paper is: some criteria of exponential stability and $L_2$ gain for multiple-input multiple-output (MIMO) switched PDE are developed in the form of LMIs and ADT signal for the first time. The advantage of the work is we generalize the application range of the related research. The proposed method is expected to provide an effective tool for stability and $H_{\mathrm{\infty }}$ control analysis of SDPS.

Keywords:

• Switched system
• distributed parameter system
• multiple-input multiple-output (MIMO)
• time delay
• average dwell time (ADT)

Acknowledgments

The authors would like to thank the helpful comments and suggestions of the Associate Editor and the anonymous reviewers, which have improved the presentation of this paper. This work was supported by the China Scholarship Council Fund (No. 201808140223) and the National Natural Science Foundation of China (No. 11661020).

Disclosure statement

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

Correction Statement

This article has been corrected with minor changes. These changes do not impact the academic content of the article

Additional information

Funding

This work was supported by the China Scholarship Council Fund [No. 201808140223] and the National Natural Science Foundation of China [No. 11661020].

Notes on contributors

Leping Bao

Leping Bao received the MS degree in the Department of Mathematics from Guizhou University in 2006, the PhD degree in control theory and control engineering from Southeast University in 2014. She is now an associate professor in the Department of Automation, Taiyuan Institute of Technology. Her research interests include analysis and design of distributed parameter switched control systems, nonlinear systems, and robotic control systems.

Pu Huang

Pu Huang received the BS degree in automation from Taiyuan Institute of Technology in 2017. He is currently pursuing the MS degree in Detection Technology and Automation Equipment with Northeast University. His research interests lie in the domain of image processing, machine learning and distributed parameter control system.

Shumin Fei

Shumin Fei received the PhD degree from Beijing University of Aeronautics and Astronautics, China in 1995. Form 1995 to 1997, he was doing postdoctoral research at Research Institute of Automation, Southeast University, China. Presently, he is a professor and doctor adviser at Southeast University. He has published more than 300 journal papers and his research interests include nonlinear systems, the delayed system, complex systems and so on.