A geometric characterization of feedforward forms

This note addresses the problem of (local) coordinates and feedback equivalence of single-input affine nonlinear systems to feedforward forms. In particular, using the notions of invariant and controlled invariant distributions we provide necessary and sufficient conditions for a general affine in control nonlinear system to be (locally) coordinates or feedback equivalent to a system in (strict) feedforward form. For illustration, the general theory is applied to a simple four-dimensional system describing the dynamics of a food-chain.