Non-linear non-interacting control with stability in discrete-time: A geometric framework

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 su fficient 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.