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Stability Analysis and Robust H∞ Controller Synthesis with Derivatives of Membership Functions for T-S Fuzzy Systems with Time-varying Delay: Input-output Stability Approach

Redouane Chaibi*, Hicham El Aiss, Ahmed El Hajjaji, and Abdelaziz Hmamed
International Journal of Control, Automation, and Systems, vol. 18, no. 7, pp.1872-1884, 2020

Abstract : This paper investigates the problem of delay dependent stability and H∞ control design with derivatives of membership functions of uncertain Takagi-Sugeno (T-S) fuzzy systems with interval time-varying delay. A model transformation is employed by considering a three-term approximation of delayed state vector. Using Scaled Small Gain (SSG) theorem and fuzzy weighting-dependent Lyapunov functions with some useful slack variables, less conservative robust stability and stabilization criteria are formulated in terms of linear matrix inequalities (LMIs), which can be easily solved by using standard numerical packages. Finally, numerical experiments are presented to illustrate the effectiveness of the proposed method.

Keyword : Input-output stability, Lyapunov-Krasovskii functional (LKF), scaled small gain theorem, TakagiSugeno (T-S) fuzzy systems, time-varying delay

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