Relaxed Non-Quadratic Stability Conditions for Takagi-Sugeno Systems with Time-Varying Delays: A Wirtinger’s Inequalities approach
Fayçal Bourahala, Kevin Guelton, Adriano Nogueira Drumond Lopes · 2019
This paper aims at proposing less conservative delay-dependent stability conditions for non-linear delayed systems described by T-S fuzzy models with interval time-varying delays. To reach this goal, an augmented Lyapunov-Krasovskii functional (LKF) containing a non-quadratic Line-Integral Lyapunov Functional (LILF) and double and triple integral terms is considered. Then, single and double integral Wirtinger's inequalities are employed to handle the derivatives of the considered LKF. Free weighting variables are also introduced from the application of the Finsler's lemma and by considering null terms. As a results, relaxed delay-dependent stability conditions are derived as linear matrix inequalities and summarized in a theorem. To show the conservatism improvement of the proposed stability conditions regarding to previous results from the literature, comparisons are made through the stability analysis of a usual numerical example of T-S system with time-varying delays.