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In this article, a signal-compensation based approach is presented to the robust output regulation problem for a class of multi-input multi-output uncertain systems with uncertain exosystems. The use of equivalent disturbance attenuation techniques permits removal of a common restriction that the exosystem which generates the reference signals and/or the disturbance signals is accurately known. The proposed robust controller is a linear-invariant one that consists of a nominal controller and a robust compensator. It is proven that the asymptotic regulation error can be made as small as desired.