In this paper linear sampled data multi-variable synthesis is considered by the use of state difference equations. Murphy and Meksuwan's “1963” of approach is generalized for multi-variable systems. The non-interaction condition limits the achievement of dead-beat response depending on the nature of the input and the order of the individual transfer functions of the system. The method is general and can be applied to any polynominal input and also when non-linearities are present just after the compensator.