Structural Relaxation Approach to H∞ Control with Quadratic Fuzzy Lyapunov Function for Continuous-Time Takagi–Sugeno Fuzzy Systems

Abstract

This paper presents an investigation of the stability analysis and ∞ control synthesis for Takagi–Sugeno fuzzy systems based on a quadratic fuzzy Lyapunov function, which incorporates second-degree information of membership functions. Instead of a multiple summation expression, the Lyapunov function and controller are designed within the structure of the membership-quadratic framework, which is a quadratic form with membership-dependent outfactors. A structural relaxation lemma is established based on zero-equality conditions through orthogonal complements and characteristics of the matrix of the quadratic form. On the basis of the proposed structural relaxation approach, the stability conditions for the analysis and synthesis are achieved through linear matrix inequalities with elaborate matrix manipulation techniques. Conceptual foundations employing high-degree membership functions are provided to generalize the structural relaxation approach. Comprehensive numerical examples that demonstrate the efficacy of the proposed approach are detailed. IEEE