Mixed H_∞ and passive control for linear switched systems via hybrid control approach

ABSTRACT

This paper investigates the mixed H_∞ and passive control problem for linear switched systems based on a hybrid control strategy. To solve this problem, first, a new performance index is proposed. This performance index can be viewed as the mixed weighted H_∞ and passivity performance. Then, the hybrid controllers are used to stabilise the switched systems. The hybrid controllers consist of dynamic output-feedback controllers for every subsystem and state updating controllers at the switching instant. The design of state updating controllers not only depends on the pre-switching subsystem and the post-switching subsystem, but also depends on the measurable output signal. The hybrid controllers proposed in this paper can include some existing ones as special cases. Combine the multiple Lyapunov functions approach with the average dwell time technique, new sufficient conditions are obtained. Under the new conditions, the closed-loop linear switched systems are globally uniformly asymptotically stable with a mixed H_∞ and passivity performance index. Moreover, the desired hybrid controllers can be constructed by solving a set of linear matrix inequalities. Finally, a numerical example and a practical example are given.

KEYWORDS:

• H_∞ control
• passive control
• linear switched systems
• average dwell time
• multiple Lyapunov functions
• hybrid control

Acknowledgments

The authors would like to thank the editors and anonymous reviewers for their valuable suggestions about our paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is supported by the Open Research Fund of Anhui Key Laboratory of Detection Technology and Energy Saving Devices, Anhui Polytechnic University [grant number 2017070503B026-A07]; Natural Science Research of Anhui higher education promotion program [grant number TSKJ2017B25]; Priming Scientific Research Foundation for the Introduction Talent in Anhui Polytechnic University [grant number 2017YQQ002]; in part by the National Natural Science Foundation of China [grant number 61374117], [grant number 61203033]; Natural Science Foundation of Anhui Province [grant number 1608085MF146]; Natural Science Research Programme of Colleges and Universities of Anhui Province [grant number KJ2016A062]; Visiting Study Foundation for Outstanding Young Talent of An'hui Educational Committee [grant number gxfxZD2016108].

Notes on contributors

Qunxian Zheng

Qunxian Zheng received the B.Eng. degree in biomedical engineering, the M.Eng. degree in biophysics, and the Ph.D. degree in circuits and systems from University of Electronic Science and Technology of China, Chengdu, in 2008, 2011, and 2016, respectively. He is currently working as a lecturer at the Anhui Polytechnic University, Wuhu. His research interests include fuzzy control and switched systems.

Youzhu Ling

Youzhu Ling received the B.Eng. degree in power plant and power system from the HeFei University of Technology in 1983, and the M.Eng. degree in engineering of power system and automation from the Harbin Institute of Technology in 1988. He is currently working as a professor at the Anhui Polytechnic University, Wuhu.

Lisheng Wei

Lisheng WEIwas born in Chaohu City, in 1978. He received his B.S. degree in automation from Anhui Polytechnic University in 2001, received the M.S. degree in flight vehicle design from China Aerospace Science and Industry Corporation 061 Base in 2004, and received the Ph.D. degree in control science and engineering from Shanghai University in 2009. Now he has been a professor with the School of Electrical Engineering, Anhui Polytechnic University. He is the author of more than 50 articles, and holds eleven patents. His research interests include image recognition and application, embedded instrumentation and system, intelligent network control theory, system and simulation, data fusion. Mr. WEI was a recipient of Rookie of the Teaching Forum Award in 2013, and the Anhui Natural Science Outstanding Paper second Award in 2010.

Hongbin Zhang

Hongbin Zhang received the B.Eng. degree in aerocraft design from Northwestern Polytechnical University, Xi’an, China, in 1999, and the M.Eng. and Ph.D. degrees in circuits and systems from the University of Electronic Science and Technology of China, Chengdu, in 2002 and 2006, respectively. He has been with the School of Electrical Engineering, University of Electronic Science and Technology of China, since 2002, where he is currently a professor. From August 2008 to August 2010, he has served as a research fellow with the Department of Manufacturing Engineering and Engineering Management, City University of Hong Kong, Kowloon, Hong Kong. His current research interests include intelligent control, autonomous cooperative control and integrated navigation.