General and Less Conservative Criteria on Stability and Stabilization of T–S Fuzzy Systems With Time-Varying Delay
Tian-Shun Peng, Hong‐Bing Zeng, Wei Wang, Xian‐Ming Zhang, Xinge Liu
Abstract
This article deals with the problem of stability and stabilization of Takagi–Sugeno (T–S) fuzzy systems with time-varying delay. First, a novel Lyapunov–Krasovskii functional is constructed, which is dependent on membership functions and takes more information on the time-varying delay into account. Next, based on an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N$</tex-math></inline-formula> -order free-matrix-based integral inequality and a switching method, a cluster of criteria on the stability and stabilization are obtained for the closed-loop system connected with switching state-feedback controllers. Then, a parameter tuning method and an iterative algorithm are devised to calculate control gains. Finally, three numerical examples including the truck-trailer system are given to show that the proposed criteria can offer less conservative results than some existing ones.