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In this paper a new robust steepest-descent algorithm for discrete-time iterative learning control is introduced for plant models with multiplicative uncertainty. A theoretical analysis of the algorithm shows that if a tuning parameter in the algorithm is selected to be sufficiently large, the algorithm will result in monotonic convergence if the plant uncertainty satisfies a positivity condition. This is a major improvement when compared to the standard steepest-descent algorithm, which lacks a mechanism for finding a balance between convergence speed and robustness. Experimental work on a gantry robot is performed to demonstrate that the algorithm results in near perfect tracking in the limit.