Abstarct: In this thesis we use a controller baxsed on a state-dependent Riccati equation (SDRE) optimal observer to control the speed of a permanent magnet synchronous motor (PMSM).First, An SDRE observer was designed to estimate the state variables and load torque. Then, a controller baxsed on estimated of state variables is proposed to calculate the control inputs for regulation the rotor speed of a PMSM. In this method, the controller is compensate to error of state estimation. The stability of the proposed method is ensure through Lyapunov's theory. The simulation of the proposed control method demonstrat its efficiency and effectiveness.