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This paper presents a robust monotonically convergent (RMC) iterative learning control (ILC) design for a class of uncertain linear discrete-time systems with non-zero constant initial error. The learning law under consideration is an anticipatory ILC. Based on a simple quadratic performance function, a sufficient condition for robust monotonic convergence of the proposed learning algorithm is presented in terms of linear matrix inequality (LMI). Finally, a simulation example is given to show the effectiveness of the proposed scheme.