Robust Adaptive Control of Fuzzy Nonlinear System via Variable Structure Control Approach

Abstract

This paper proposed a novel fuzzy Variable Structure Controller (VSC) design for uncertain T-S fuzzy system, while neither assuming the control matrices of each local T-S model to be same nor knowing the priori information of the upper norm-bounds of uncertainties. The existence condition of desired sliding surfaces and the asymptotical stability of the reduced-order equivalent sliding-mode dynamics are firstly derived by solving a set of linear matrix inequalities (LMIs). After the establishment of the local T-S model, the upper norm-bounds of uncertainties and modeling errors between the original and local systems are estimated. Then, the designed VSC controller composes of a state-feedback control term and an adaptive switching-feedback control term, which are achieved based on the Lyapunov function method. Finally, a numerical example is illustrated in order to show the effectiveness of the proposed methods.