This technical note proposes a robust iterative learning control (ILC) strategy to regulate iteratively-operated, finite-duration nonrepetitive systems characterized by iteration-varying uncertainties in initial states, external disturbances, plant model matrices and desired reference trajectories. Our convergence analysis exploits results on input-to-state stability of discrete parameterized systems. For a class of multiple-input, multiple-output discrete-time linear systems, with all iteration-varying uncertainties bounded, we give one condition that ensures boundedness of all system trajectories and an additional, second condition that ensures convergence of tracking error. Notably, we do not require the standard ILC contraction mapping requirement to hold at each iteration. Moreover, we show that it is possible to achieve perfect output tracking if the iteration-varying uncertainties all converge with increasing iteration.