Output-feedback control for discrete-time switched systems via non-monotonic switched Lyapunov function approach

Abstract

This paper investigates the output-feedback control for discrete-time switched linear systems. By extending the methodology of switched Lyapunov functions (SLF), a non-monotonic SLF approach is proposed to analyse the stability of the resulting closed-loop system under arbitrary switching. This approach relaxes the requirement of monotonicity to conventional SLF approach, and hence it will lead to less conservative results. First, the stability of discrete-time switched systems is analysed, and then an output-feedback controller design method is proposed based on the obtained stability results. The controller design problem is formulated in term of LMIs, and relaxed variables are introduced in the synthesis conditions to improve the design freedom. Finally, three examples are used to verify the effectiveness and application potential of the proposed methods.

Keywords:

• Discrete-time switched system
• non-monotonic switched Lyapunov function approach
• output-feedback control
• arbitrary switching

Disclosure statement

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

Additional information

Notes on contributors

Sicheng Shan

Sicheng Shan was born in JiangxiProvince, China, in 1999. He received the B.S. degree in Electrical Engineering and Automation from the Shanghai University of Engineering Science, Shanghai, China, in 2020, and he is currently a master student in the Shanghai University of Engineering Science. His research interests include switched system control and their applications in Power Electronics and Industrial Systems.

Yanhui Tong

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

Mingyuan Zhai

Mingyuan Zhai received his B.S. degree in Automation and M.S. degree in Power Electronics and Transmission from the Northeastern University, Shenyang, China, in 2007 and 2009, respectively. Since 2009, he has been working in the Flight Control Department of Shenyang Aircraft Design and Research Institute, Shenyang, China, as a senior control engineer. His research interest mainly includes the design of advanced flight control systems.

Dongmei Xu

Dongmei Xu received the B.S. degree in Electronic and Information Engineering from the Nanjing University of Technology, Nanjing, China, the M.S. degree in Communication and Information System from the China University of Mining Technology, Xuzhou, China, and the Ph.D. degree in Control Engineering with the University of Duisburg-Essen, Duisburg, Germany, in 2007, 2010 and 2014, respectively. She is currently a lecturer of the 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.