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The mathematical models of the electric power steering system were formed theoretically, and the state-space expression of the stochastic dynamic system was performed first. Then the LQG state feedback controller was designed with the minimum, and a discrete Kalman filter was proposed based on the optimal estimation theory. Finally, the simulation results showed that this optimal control method could attenuate the random road excitation, torque sensor measurement noises, model errors and disturbances reduce oscillations that might occur in the steering column, provide satisfied road feeling for drivers, the controller improves the robust performance of EPS system and enhances maneuverability of the vehicle.