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In this work we focus on the iterative learning control (ILC) design problem for linear discrete-time systems with iteration-varying factors,including reference trajectories,initial states,and exogenous disturbances.First,multiple high-order internal models (HOIMs) are given for various iteration-varying factors.Second,a new ILC scheme is constructed according to an augmented HOIM that is the aggregation of all HOIMs.Third,the HOIM-based ILC is transformed into a controller design problem of 2-D Roesser model.Fourth,the H-inf performance of 2-D Roesser model is studied under a non-zero boundary condition.Then,a HOIM-based ILC design criterion is presented to achieve perfect tracking and 2-D H-inf tracking performance which yields a high-order ILC (HO-ILC).Utilizing information provided by multiple HOIMs,it is shown that HO-ILC laws outperform low-order ILC (LO-ILC) laws in presence of iteration-varying factors.In addition,a composite HOIM-based law is proposed to improve the initial phase tracking performance.Finally,two numerical examples are given to illustrate the efficiency of the proposed HOIM-based ILC design method.