Stabilization of T-S fuzzy fractional rectangular descriptor time-delay system

Abstract

This paper focuses on the stabilization of the T-S fuzzy fractional rectangular descriptor time-delay system. To convert the fuzzy rectangular time-delay system into the fuzzy square time-delay system, a suitable dynamic compensator of proportional and derivative type is constructed, and the admissibility of the resultant square closed-loop system is enough to guarantee the stabilization of the nonlinear rectangular descriptor time-delay system. A sufficient condition is derived to ensure the stabilization for the considered system and the dynamic compensator parameters can be computed by solving the corresponding linear matrix inequalities (LMIs). A numerical example is provided to manifest the theoretical result.

Keywords:

• Rectangular descriptor
• T-S fuzzy system
• fractional-order
• LMIs

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is supported by the National Natural Science Foundation of China [grant no. 61773004], the Science and Technology Research Program of Chongqing Municipal Education Commission of China [grant no. KJZD-M202000701], and the Graduate Scientific Research and Innovation Foundation of Chongqing Jiaotong University [grant no. 2020S0049].

Notes on contributors

Qian Wu

Qian Wu was born in 1996. She received the B.S. degree in Engineering Management in 2018 and is working toward the M.E. degree in Management Science and Engineering, both from Chongqing Jiaotong University, Chongqing, China. Her current research interest is the stability theory of singular systems.

Qiankun Song

Qiankun Song was born in 1964. He received the B.S. degree in Mathematics in 1986 from Sichuan Normal University, Chengdu, China, the M.S. degree in Applied Mathematics in 1996 from Northwestern Polytechnical University, Xi'an, China, and the Ph. D. degree in Applied Mathematics in 2010 from Sichuan University, Chengdu, China. From July 1986 to December 2000, he was with Department of Mathematics, Sichuan University of Science and Engineering, Sichuan, China. From January 2001 to June 2006, he was with the Department of Mathematics, Huzhou University, Zhejiang, China. In July 2006, he moved to the Department of Mathematics, Chongqing Jiaotong University, Chongqing, China. He is currently a Professor at Chongqing Jiaotong University. He is currently serving as an Editorial Board Member for Neurocomputing, Neural Processing Letters, Systems Science and Control Engineering, Journal of Applied Mathematics, British Journal of Mathematics & Computer Science, ISRN Applied Mathematics, Asian Journal of Mathematics and Computer Research, and a reviewer for Mathematical Reviews. He is the author or coauthor of more than 80 journal papers and two edited books. His current research interests include stability theory of neural networks and chaos synchronization.

Zhenjiang Zhao

Zhenjiang Zhao was born in 1962. He received the B.S. degree in Mathematics in 1984 from Kashgar Teachers College, Kashgar, China, the M.S. degree in Applied Mathematics in 1998 from Okayama University, Okayama, Japan. He is currently a Professor at Huzhou University. He is the author or coauthor of more than 30 journal papers. His current research interests include stability theory of neural networks.

Yurong Liu

Yurong Liu received his B.S. degree in Mathematics from Suzhou University, Suzhou, China, in 1986, the M.S. degree in Applied Mathematics from Nanjing University of Science and Technology, Nanjing, China, in 1989, and the Ph.D. degree in Applied Mathematics from Suzhou University, Suzhou, China, in 2000. He is currently a Professor at Yangzhou University, China. He has published more than 50 papers in refereed international journals. His current interests include neural networks, complex networks, nonlinear dynamics, time-delay systems, multiagent systems, and chaotic dynamics.

Fuad E. Alsaadi

Fuad E. Alsaadi received the B.S. and M.S. degrees in electronic and communication from King Abdulaziz University, Jeddah, Saudi Arabia, in 1996 and 2002. He then received the Ph.D. degree in optical wireless communication systems from the University of Leeds, Leeds, UK, in 2011. Between 1996 and 2005, he worked in Jeddah as a communication instructor in the College of Electronics & Communication. He was a lecturer in the Faculty of Engineering in King Abdulaziz University, Jeddah, Saudi Arabia in 2005. He is currently an assistant professor of the Electrical and Computer Engineering Department within the Faculty of Engineering, King Abdulaziz University, Jeddah, Saudi Arabia. He published widely in the top IEEE communications conferences and journals and has received the Carter award, University of Leeds for the best PhD. He has research interests in optical systems and networks, signal processing, synchronization and systems design.