Modeling error occurs in linearizing the real (nonlinear) system into the (linear) T-S fuzzy model, and the existence of uncertainties in the real system including external disturbances. This paper deals with the T-S fuzzy model with modeling error in order to improve the control performance. As a result, an adaptive controller that consists of two parts: one is obtained by solving certain Linear Matrix Inequalities (LMIs) (fixed part) and the other is acquired by the fuzzy approximator in which the related parameters are tuned by adaptive law (variable part), is proposed. The proposed controller can guarantee all signals involved in the closed-loop system uniformly ultimately bounded.
Keywords: T-S fuzzy model, modeling error, adaptive control, LMIs