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In this work, an iterative learning controller applying to linear discrete-time multivariable systems with variable initial conditions is investigated based on two-dimensional (2-D) system theory. The work first introduces a 2-D tracking error system and shows the effect of tracking errors against variable initial conditions. The sufficient conditions for the convergence of the learning control rules are derived and discussed. Based on the proposed iterative learning control (ILC) rule, we have shown that the convergence of the learning rule is guaranteed with less restriction. An improved ILC rule is proposed. As a result, the convergence is robust with respect to small perturbations of the system parameters. Two numerical simulation examples are used to validate the effectiveness of the proposed methodologies.