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First, the ILC process is transformed into an equivalent discrete linear repetitive process. Then, with the help of the generalized Kalman\u2013Yakubovich\u2013Popov lemma, the issue of a robust control law design algorithm in the process model is converted into the problem of solutions to the corresponding linear matrix inequality conditions. This procedure not only meets the robust performance specifications along the trial, but also guarantees the monotonic converge of the trial-to-trial error dynamics over finite frequency ranges. Finally, the simulations for a direct current servo motor system are adopted to show the effectiveness and superiority of the proposed method. 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