The problem of forcing the output of a multivariate sampled-data system to zero in a minimum number of time steps is discussed. The solution to the posed problem is given as a linear state feedback. The zeros of the system are contained among the poles of the closed-loop system. The performance of the closed-loop system will be unsatisfactory if any of these zeros are located close to or outside the unit circle. In this case suboptimal dead-beat controllers are derived.