Exact linearizations of input-output systems

The problem of transforming non-linear systems to linear systems is receiving much attention in the literature. In this paper, we present necessary and sufficient conditions such that a non-linear control system with output can be equivalent to a linear control system with linear output that is controllable and observable. The conditions depend on certain Lie derivatives of the output and can be verified in a finite number of steps. For simplicity, we consider only the single input/single output case.