In this paper we consider the problem of output deadbeat control with internal stability (ODCIS) in discrete-time linear multivariable systems which include uncontrollable external inputs. First, we consider the case in which the state feedback is allowed. It is shown that the problem is solvable if and only if the state space can be decomposed into a controllable subspace of (A, B) and an (A, B)-invariant subspace in Ker D. The minimal number of steps for attaining the deadbeat control is also derived. A procedure for computing the minimal-time state feedback control law for ODCIS is given.
Next, we generalize these results to the case in which only the output feedback is allowed. The solvability condition, the minimal number of steps and the procedure for synthesizing the minimal order deadbeat observer for attaining the minimal-time ODCIS are shown. An illustrative example is given to show the feasibility of the algorithm.