For a class of uncertain discrete repetitive process with the actuator fault, an iterative learning fault-tolerant control algorithm in the finite frequency range is proposed. By defining the equivalent two dimensional model and fault coefficient matrix for the output tracking system, the passive fault-tolerant controller with the time axis and batch axis is designed at the same time. Then based on the Kalman-Yakubovich-Popov(KYP) lemma, the sufficient and necessary condition for the
stability of the repetitive control system is given in terms of the linear matrix inequality technology in the whole frequency and division frequency range respectively, so that the fault tolerant performance of the fault system can be guaranteed both in time and frequency domain. Finally, the injection speed control simulation of the repetitive injection molding process verifies the effectiveness of the frequency division control algorithm.