Decomposition and equivalence of general nonlinear dynamical control systems

Projection and equivalence concepts havebeen widely studied in the literature. In the presentpaper two nonlinear systems with the same numberof inputs, but not the same number of state variables,are considered. Under mild assumptions, necessary andsufficient conditions are given for the existence of asubmersion such that the higher dimensional systemprojects locally onto the other one. The solution tothis problem has relevant applications, for instance inrobotics. It includes as a special case the equivalenceof nonlinear systems with no particular structure.