New insight into admissibility analysis for singular systems with time-varying delays

Abstract

This paper focuses on the admissibility analysis of singular systems with time-varying delays. The goal is to obtain admissibility criterion with less conservatism and fewer decision variables. After decomposing singular systems into differential subsystems and algebraic ones, an improved augmented Lyapunov–Krasovskii functional is established according to decomposed state vectors. Then, combining the auxiliary function-based inequality and the extended reciprocally convex matrix method, a less conservative admissibility criterion with fewer decision variables is obtained. Finally, a numerical example verifies the reduced conservatism and calculation burden of the presented method.

Keywords:

• Singular systems
• time-varying delays
• admissibility analysis
• Lyapunov–Krasovskii functional

Disclosure statement

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

Additional information

Funding

This work was supported in part by the National Natural Science Foundation of China [grant number 61973284] and the 111 project (Higher Education Discipline Innovation Project) [grant number B17040].

Notes on contributors

Yang Li

Yang Li received the B.S. degree from China University of Geosciences, Wuhan, China, in 2019. He is currently pursuing the M.S. degree in control science and engineering with the China University of Geosciences, Wuhan. His current research interests include singular systems and time-delay systems.

Yong He

Yong He received the B.S. and M.S. degrees in applied mathematics and the Ph.D. degree in control theory and control engineering from Central South University (CSU), Changsha, China, in 1991, 1994, and 2004, respectively. He was a Lecturer with the School of Mathematics and Statistics, CSU, and then a Professor with the School of Information Science and Engineering, CSU, from 1994 to 2014. He was a Research Fellow with the Department of Electrical and Computer Engineering, National University of Singapore, Singapore, from 2005 to 2006, and the Faculty of Advanced Technology, University of Glamorgan, Glamorgan, UK, from 2006 to 2007. He joined China University of Geosciences, Wuhan, China, in 2014, where he is currently a Professor with the School of Automation. His current research interests include time-delay systems and networked control systems.