Stability and Stabilization of T-S Fuzzy Systems With Time-Varying Delays via Delay-Product-Type Functional Method

• Published in: IEEE transactions on cybernetics Vol. 50; no. 6; pp. 2580 - 2589
• Main Authors: Lian, Zhi, He, Yong, Zhang, Chuan-Ke, Wu, Min
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.06.2020; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Control stability; Control systems design; Delay; Delay-product-type functional; Delays; extended reciprocally convex matrix inequality; Feedback control; Fuzzy systems; Linear matrix inequalities; Stability criteria; Stabilization; State vectors; Symmetric matrices; time-varying delay; Time-varying systems; T–S fuzzy system
• ISSN: 2168-2267; 2168-2275
• DOI: 10.1109/TCYB.2018.2890425

This paper is concerned with the stability and stabilization problems of T-S fuzzy systems with time-varying delays. The purpose is to develop a new state-feedback controller design method with less conservatism. First, a novel Lyapunov-Krasovskii functional is constructed by combining delay-product-type functional method together with the state vector augmentation. By utilizing Wirtinger-based integral inequality and an extended reciprocally convex matrix inequality, a less conservative delay-dependent stability condition is developed. Then, the corresponding controller design method for the closed-loop delayed fuzzy system is derived based on parallel distributed compensation scheme. Finally, two classic numerical examples are given to show the effectiveness and merits of the proposed approaches.