This paper proposes a new fuzzy speed controller based on the Takagi-Sugeno fuzzy method to achieve a robust speed control of a permanent magnet synchronous motor(PMSM). The proposed controller requires the information of the load torque, so the second-order load torque observer is used to estimate it. The LMI condition is derived for the existence of the proposed fuzzy speed controller, and the LMI parameterization to calculate the gain matrices of the controller is provided. It is proven that the augmented control system including the fuzzy speed controller and the load torque observer is exponentially stable. To evaluate the performance of the proposed fuzzy speed controller, the simulation and experimental results are presented under motor parameter and load torque variations. Finally, it is clearly verified that the proposed control method can be used to accurately control the speed of a permanent magnet synchronous motor.