The paper displays a receding horizon stabilization and output tracking schemes for time-varying discrete linear systems with uncertainties. The finite time component is based on a maxmin

${H}^{\infty}$ performance index. The method follows standard approaches available for the continuous time case, overcoming however, the subtle points induced by the jumps due to the discrete time. Illuminating numerical examples, based on a discretization of a second order equation, describing a position servo system, are displayed; the performance of the proposed scheme is compared with an infinite time horizon scheme.