The pulse width modulation (PWM) converter controlled by hysteresis is strong nonlinear link, thus making it
difficult to improve current control quality by using optimal control and normal linear processing. Therefore, the hysteresis current control principle, the harmonic linearization and stability are analyzed, and the transfer function of hysteresis current control and the relationships between time-delay, width of hysteresis and the other parameters are obtained. The method combing harmonic linearization and integral time absolute error (ITAE) optimal control to realize the PWM converters’ optimal control is proposed according to the hysteresis current control’s characteristics. The Matlab simulation results show the effectiveness of the method.