In recent years, there have been significant advances in the study of the stability analysis and controller synthesis for the so-called Takagi-Sugeno (T-S) fuzzy systems, which have been used to represent certain complex nonlinear systems. Based on the T-S fuzzy model, the controller can be obtained by solving certain Linear Matrix Inequalities (LMIs). However, only a few results concerning the modeling error, which often is referred to as reconstruction error, between the real system to be controlled and its T-S fuzzy model, are reported. In this paper, the reconstruction error, which consists of parameter uncertainties and external disturbance, is considered. As a result, we arrive at an adaptive controller that has two parts: one is obtained by solving certain LMIs (fixed part) and another one is acquired by an adaptive law (variable part). The proposed controller can guarantee the control state to converge and uniformly bounded while maintaining all the signals involved stable.
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