Preliminaries on almost-controlled invariance for single-input nonlinear systems

The purpose of this study is to introduce a concept of almost-controlled invariant distributions of (single-input) nonlinear systems. The definition proposed is one of the equivalent characterizations of linear almost-controlled invariance. An approach for solving the almost disturbance decoupling problem for single-input-single-output nonlinear systems is given. Part of this method is essentially on the use of the notion of almost-controlled invariance and would appear to be connected with the idea of singular perturbations methods