An elliptical attracting law which can effectively reduce chattering is proposed for the periodic tracking problem of discrete time systems. The disturbance of the extended state observe technique is used to effectively reduce the unknown disturbance of the system, and the periodic disturbance is able to be completely rejected by the repetitive control technique. In order to evaluate the tracking performance of the closed-loop system, the expressions of the monotone decreasing region, the absolute attractive layer, the boundary of the steady-state error and the maximum step size of the system tracking error entering the steady state are derived in details. Simulation and experimental results of a linear servo motor system are presented to verify effectiveness of the proposed repetitive control method.