Quadratically convex combination approach to stability of T-S fuzzy systems with time-varying delay

This paper develops a novel stability analysis method for Takagi-Sugeno (T-S) fuzzy systems with time-varying delay. New delay-dependent stability criteria in terms of linear matrix inequalities for time-varying delayed T-S fuzzy systems are derived by the newly proposed augmented Lyapunov-Krasovski (L-K) functional. This functional contains the cross terms of variables and quadratic terms multiplied by a higher degree scalar function. Different from previous results, our derivation applies the idea of second-order convex combination, and the property of quadratic convex function without resorting to the Jensen's inequality. Two numerical examples are provided to verify the effectiveness of the presented results. (C) 2013 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.