On delay-dependent stability conditions for Takagi–Sugeno fuzzy systems

This paper presents new less conservative stability analysis conditions for Takagi–Sugeno fuzzy systems subject to interval time-varying delay. The methodology is based on the direct Lyapunov method allied with an appropriate Lyapunov–Krasovskii functional choice and the use of the integral inequalities, Finsler lemma, Newton–Leibniz formula manipulations and convex combination properties. Particularly, the main result differs from previous ones since the positiveness of the Lyapunov–Krasovskii functional is guaranteed by new relaxed conditions. Two examples illustrate the effectiveness of the proposed methodology.