In this article, a discrete-time design of higher-order repetitive sliding mode controller (HO-RSMC) for uncertain linear systems with time-varying periodic disturbances is presented. In the design, a higher-order repetitive control (HORC) is employed to significantly suppress the periodic exogenous disturbance with period variation. The HORC-based control system offers a slow transient response due to the multiple control delays. Moreover, since the system stability is easily affected by model uncertainties, an output-feedback sliding mode controller (SMC) is added to overcome the shortcomings of HORC. Stability analysis of the resulting closed-loop system is rigorously provided. The simulation results and comparison studies confirm the effectiveness and good performance of the proposed design.
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