Nonfragile H∞ tracking control strategies for classes of linear and bilinear uncertain Takagi-Sugeno fuzzy systems

Abstract

This paper presents fuzzy tracking control strategies for classes of linear and bilinear Takagi-Sugeno Fuzzy System with Uncertainties and Disturbances (T-S FSUD). For both classes, the Lyapunov direct approach and the parallel distributed compensation concept are used to design nonfragile H∞ tracking controllers, which ensure the robust asymptotic stability of augmented systems despite the presence of parameter uncertainties, external disturbances, and controllers fragility. Besides that, based on the Schur complement, the separation lemma, and through some variable transformations, sufficient stability conditions of each augmented T-S FSUD are established and formulated in terms of linear matrix inequalities. Finally, numerical simulations are carried out to demonstrate the validity and the applicability of designed control schemes on tracking control of an inverted pendulum and a nonlinear mechanical system.