The aim of the paper is to set the non-linear non-interacting control problem with stability in discrete time in a correct geometric framework so providing a solution which recalls the continuous approach, and to point out the peculiarities of discrete time dynamics. Geometric necessary and sufficient conditions for the solvability of the problem are given, and a constructive method figures out the regular static state feedback solution. It is shown that if the given dynamics is feedback equivalent to a decoupled system characterized by an invertible drift, the computation of the distributions involved can be carried out in a simple and elegant way. The main results are thus proved exhaustively in this case and then generalized to submersive systems.