A relation between different approaches to input-output linearization via feedback (Q1068036)

In recent years state (feedback) transformations for nonlinear affine control systems have been studied from various viewpoints. For example, one can study the problem whether or not the system is linear after applying a suitable state feedback and state space transformation. Or, weaker, when is it possible to apply state feedback such that the external behavior of the system is linear? Another related question is when is it possible to immerse (''map into'') the nonlinear system into a linear system? The present paper deals with the last two questions and it is shown by direct inspection that the conditions for input-output linearizability coincide with those for immersed linearization provided that the original nonlinear system is right invertible.