Improved stability criteria for T–S fuzzy systems with time‐varying delay via convex analysis approach

Abstract

This study is concerned with stability analysis for Takagi–Sugeno (T–S) fuzzy systems with time‐varying delay. By applying the idea of scalar function and augmented vectors, dealing with the positivity of a functional, a novel simple Lyapunov–Krasovskii functional is established. Then, fuzzy‐weighting dependent matrices and the reciprocally convex approach are introduced to deal with two integral parts, convex analysis approach is used to solve the useful terms (which are ignored in previous methods), with the above methods some less conservative stability criteria is obtained. Finally, three numerical examples are provided to show the effectiveness and improvements of the proposed conditions.