Congruent-Transformation-Based Stability Criterion of T-S Fuzzy Systems With Time-Varying Delay via the Generalized Line-Integral Lyapunov Function

This paper is concerned with the stability analysis of Takagi-Sugeno (T-S) fuzzy systems with time-varying delays. First, by constructing a generalized line-integral Lyapunov function (GLILF), applying the free-matrix-based inequality and the delay-derivative-dependent free-weighting-matrices method, a basic stability criterion is derived. Besides, the structure of the matrices in the stability criterion is reconstructed through congruent transformation, and an improved stability criterion is derived accordingly. To clarify the advancement of the proposed method, a stability condition is given without the GLILF. Finally, two numerical examples and a practical example are applied to show the advancement and merits of the presented method.