In this paper, a solution is given to the problem of dead-beat ripple-
free tracking for a multivariable multirate sampled-data system. The s
olution of such a problem is reduced to the solution of a dead-beat tr
acking problem for the corresponding discrete-time periodic system by
introducing an additional requirement of dead-beat control for the con
trol input of the multirate sampled-data system. The conditions for th
e problem solvability include the existence of a continuous-time inter
nal model of all reference signals in the continuous-time plant. The d
esign procedure of the periodic discrete-time compensator reduces to t
he design of a dead-beat periodic controller.