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This paper proposed an integral sliding mode control scheme based on repetitive control for uncertain repetitive processes with the presence of matched uncertainties, external disturbances and norm-bounded nonlinearities. A new method based on the combination of repetitive control and sliding mode approach is studied in order to use the robustness sensibility property of the sliding mode control to matched uncertainties and disturbances and to cancel gradually tracking error for periodic processes. A sufficient condition of the existence of sliding mode is studied based on basic repetitive control and a sliding mode controller is synthesized through linear matrix inequalities, which guarantees the stability along the periods of the controlled closed-loop process and the reachability of the sliding surface is ensured. Then, an adaptive integral sliding mode controller is synthesized to improve performances of the proposed control scheme. The effectiveness of the proposed controlled design schemes is proved by the use of a third order uncertain mechanical system and the simulation results using the new approaches give good performances.

Repetitive Control based on Integral Sliding Mode Control of Matched Uncertain Systems