New algebraic-geometric conditions for the linearization by input-output injection

The goal of this paper is twofold. It unifies and generalizes existing results on input-output injection linearization of nonlinear systems. The problem is solved as a realization problem since it is based on the analysis of the structure of the input-output differential equation. The necessary and sufficient conditions are derived from a simplified and constructive procedure. For clarity, the paper is limited to the case of single output systems. Exterior differential systems are extensively used throughout the paper, giving constructive conditions.