Stability analysis of T–S fuzzy systems with time-varying delay via parameter-dependent reciprocally convex inequality

ABSTRACT

The stability problem of T–S fuzzy systems with time-varying delay is investigated in this article. The purpose is to establish the less conservative stability conditions for T–S fuzzy systems with time-varying delays. Firstly, a parameter-dependent reciprocally convex inequality is proposed to improve the estimation accuracy of reciprocal convex terms. Secondly, based on the line-integral Lyapunov–Krasovskii (L–K) function and the developed parameter-dependent reciprocally convex inequality, a less conservative stability condition is established. Finally, two examples are used to verify the feasibility and superiority of the proposed method.

KEYWORDS:

• T–S fuzzy systems
• Lyapunov–Krasovskii functional
• stability conditions
• time-varying delay
• reciprocally convex inequality

Disclosure statement

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

Data availability statement

The authors confirm that data and materials that support the results or analyses presented in this paper are freely available upon request.

Additional information

Funding

This work was supported in part by the National Natural Science Foundation of China [grant numbers 62273079, 61873056, 61621004 and 61420106016]; the Fundamental Research Funds for the Central Universities in China [grant numbers N2004002, N2104005 and N182608004]; and the Research Fund of State Key Laboratory of Synthetical Automation for Process Industries in China [grant number 2013ZCX01].

Notes on contributors

Huichao Lin

Huichao Lin received the B.S. degree in automation, the M.S. degree in control theory and control engineering from the Hunan University of Technology, Zhuzhou, China, in 2018 and 2021, respectively. He is currently pursuing the Ph.D. degree in control science and engineering with Northeastern University, Shenyang, China. His current research interests include time-delay system and multi-agent systems.

Jiuxiang Dong

Jiuxiang Dong received the B.S. degree in mathematics and applied mathematics, the M.S. degree in applied mathematics from Liaoning Normal University, Dalian, China, in 2001 and 2004, respectively, and the Ph.D. degree in navigation guidance and control from Northeastern University, Shenyang, China, in 2009. He is currently a Professor with the College of Information Science and Engineering, Northeastern University. His research interests include fuzzy control, robust control, and reliable control. Dr. Dong is an Associate Editor for the International Journal of Control, Automation, and Systems.