Finite-time H_∞ control for discrete-time switched systems with admissible edge-dependent average dwell time

Abstract

This paper is concerned with finite-time $H_{\mathrm{\infty }}$ control for discrete-time switched linear systems via admissible edge-dependent switching. The admissible edge-dependent average dwell-time (AED–ADT) is employed to identify a class of constrained switching signals for the resulting closed-loop system. Moreover, multiple discontinuous Lyapunov function (MDLF) approach, which is less conservative than the traditional multiple Lyapunov function (MLF) method, is used to analyse the closed-loop stability and $H_{\mathrm{\infty }}$ performance by incorporating the idea of AED–ADT. By constructing the MDLFs in quadratic forms, a synthesis condition for finite-time bounded control is first proposed, then a synthesis condition for finite-time $H_{\mathrm{\infty }}$ control is further developed based on the obtained result. Finally, two simulation examples are given to verify the effectiveness and practicability of the presented control synthesis method.

Keywords:

• Admissible edge-dependent average dwell time
• finite-time $H_{\mathrm{\infty }}$ control
• multiple discontinuous Lyapunov function approach
• discrete-time switched systems

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Notes on contributors

Hailong Wang

Hailong Wang was born in Henan Province, China, in 1994. He received his B.E. degree in Electrical Engineering and Automation from Henan Normal University in 2017, and he is currently a master student in Shanghai University of Engineering Science. His research interests include switched system control and it's applications in power electronics.

Yanhui Tong

Yanhui Tong received his B.S. and M.S. degrees in Automation and Navigation, Guidance and Control from Northeastern University, Shenyang, China, in 2007 and 2009, respectively, and the Ph.D. degree in Control Science and Engineering from Space Control and Inertial Technology Center, Harbin Institute of Technology, China, in 2013. From Nov. 2013 to Sept. 2017, he worked in Shanghai Institute of Electro-Mechanical Engineering, Shanghai Academy of Spaceflight Technology, China, as a control system engineer. He is currently a lecturer affiliated with School of Electronic and Electrical Engineering, Shanghai University of Engineering Science, China. His research interests include switched system control, model predictive control and their applications in flight control systems and industrial systems.

Dongmei Xu

Dongmei Xu received the B.S. degree in Electronic & Information Engineering from Nanjing University of Technology, Nanjing, China, the M.Sc. degree in Communication & Information System from China University of Mining Technology, Xuzhou, China, and the Ph.D. degree in control engineering with University of Duisburg-Essen, Duisburg, Germany, in 2007, 2010 and 2014, respectively. She is currently a lecture of School of Electronic and Electrical Engineering, Shanghai University of Engineering Science, China. Her current research interests include fault diagnosis and fault tolerant control of networked control systems.

Wanqing Song

Wanqing Song received the B.S. degree in Automation from the Inner Mongolia University of Science and Technology, China, in 1983, the M.S. degree in Control Science and Engineering from the University of Science and Technology Beijing, China, in 1990, and the Ph.D. degree in Mechanical Manufacturing and Automation from Donghua University, China, in 2010. He is currently a professor of Shanghai University of Engineering Science. His main research interests include condition monitor and fault diagnosis.