This paper presents a repetitive control method for discrete-time systems, where the reference signal is periodic. attracting law is suggested to form ideal error dynamics, and the repetitive controller design is carried out based on the ideal error dynamics. Through replacing the sign function with the saturation function, the chatting can be eliminated, and complete rejection for periodic disturbances can be achieved. To characterize the error dynamics, the monotonically decreasing region, the attractive layer, and the steady-state error band are defined, and the bounds for three layers are derived respectively. Numerical simulation and experiment results on a DC/AC converter are presented to show the effectiveness of the proposed repetitive control method.