A comprehensive solution to the problem of the robust output min-max control for discrete uncertain MIMO systems with matched uncertainties is presented in this paper. In the literature, state-dependent Lyapunov and Riccati min-max controllers were treated independently and the existence problem of the output min-max controllers has not been fully resolved. In this paper, both Lyapunov- and Riccati-based min-max output control laws are treated, and a simple criterion for the existence of a min-max output controller is provided It is shown that when the criterion is satisfied, both Riccati-and Lyapunov-based output min-max controllers exist. The first controller is applied directly to the given system, while the latter controller is applied to the given system closed with a suitable feedback. Moreover, it is shown that both overall controllers are identical. In addition, an alternative criterion for the existence of a Lyapunov-based min-max output control, in terms of discrete positive real properties of the system, is derived.