A finsler-based result for the stability analysis of Takagi-Sugeno fuzzy models with interval time-varying delays

This paper focuses on the stability analysis of Takagi-Sugeno fuzzy models involving interval time-varying delays in their states. New relaxed delay-dependent conditions are proposed in terms of Linear Matrix Inequalities (LMIs), which include both the lower and the upper bounds of the interval time-varying delay. These conditions are obtained from a convenient choice of a Lyapunov-Krasovskii functional (LKF) to take into account both the lower and upper bounds of the interval time-varying delay, the application of the Finsler's lemma and the introduction of free decision variables thank to the Leibniz-Newton formula and some extensions of the Jensen's inequality. A numerical example is provided to illustrate the effectiveness of the proposed LMI-based conditions with respect to previous results.