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This study introduces a fuzzy linear control design method for nonlinear systems with optimal H 1 robustness performance. First, the Takagi and Sugeno fuzzy linear model is employed to approximate a nonlinear system. Next, based on the fuzzy linear model, a fuzzy controller is developed to stabilize the nonlinear system, and at the same time the effect of external disturbance on control performance is attenuated to a minimum level. Thus based on the fuzzy linear model, H 1 performance design can be achieved in nonlinear control systems. In the proposed fuzzy linear control method, the fuzzy linear model provides rough control to approximate the nonlinear control system, while the H 1 scheme provides precise control to achieve the optimal robustness performance. Linear matrix inequality (LMI) techniques are employed to solve this robust fuzzy control problem. In the case that state variables are unavailable, a fuzzy observer-based H 1 control is also proposed to achieve a robust optimization design for nonlinear systems. A simulation example is given to illustrate the performance of the proposed design method.Index Terms-H 1 robust control, linear matrix inequality, nonlinear fuzzy observer, Takagi-Sugeno fuzzy control.

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In this correspondence, we show that the rule base implemented in the aforementioned paper cannot act as a universal approximator. Furthermore, we show by simulation that the robot example reported in the paper can be effectively controlled without need for the fuzzy component.