This article is mainly concerned with uncertain systems subject to periodic disturbances with known periodicity, and the methodology of discrete variable structure repetitive control is applied to address the control problem. The notion of quasi-sliding mode (QSM) is reviewed in this article. Switching function dynamics obtained with the proposed repetitive control strategies are desirable to govern both reaching phase and sliding phase. For characterising the switching-function dynamics, detailed estimation results of both attractive layer bound and QSM band are given, with which the repetitive controllers can be designed to ensure closed-loop robust stability, and achieve perfect tracking in the presence of periodic perturbations. As more knowledge about the periodicity is known, partial-period repetitive control schemes are presented for reducing memory occupation. Numerical simulation and experiment are carried out to verify the theoretical results.