A new approach to deadbeat control of a class of multivariable non-linear time-varying systems is presented. The approach enables us to find a non-linear control law, minimal positive integer N and a piecewise-constant control input vector subjected to constraints such that the output of closed-loop system coincides with given reference vectorr(l) for ≥NT, where r(<) represents the class of vector functions which can be generated in linear time-invariant systems, T is a given sampling period.