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A new design approach for an adaptive fuzzy sliding mode controller (AFSMC) for linear systems with mismatched time-varying uncertainties is presented. The coefficient matrix of the sliding function can be designed to satisfy a sliding coefficient matching condition provided time-varying uncertainties are bounded. With the sliding coefficient matching condition satisfied, an AFSMC is proposed to stabilize the uncertain system. The parameters of output fuzzy sets in the fuzzy mechanism are on-line adapted to improve the performance of the fuzzy sliding mode control system. The bounds of uncertainties are not required to be known in advance for the AFSMC. Stability of the fuzzy control system is guaranteed and the system is shown to be invariant on the sliding surface. Moreover, chattering around the sliding surface in sliding mode control can be reduced by the proposed design approach. Simulation results are included to illustrate the effectiveness of the proposed AFSMC.
Tao et al. (Thu,) studied this question.