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A novel robust indirect adaptive fuzzy control scheme based on fuzzy basis functions is proposed via linear matrix inequality (LMI) technique for the single input single output (SISO) nonlinear system. A robust control compensator is derived to offset the effect of uncertainties. It can be shown that the effect of the external disturbance on the tracking error can be attenuated to prescribed level and then the H infin control performance is achieved. Simulations demonstrate that the algorithm of on-line self-adjusting by means of altering the fuzzy rules basis makes the control system stable globally and the tracking control has been achieved.