Internal dynamics of flat nonlinear SISO systems with respect to a non-flat output

In this article, the internal dynamics of flat nonlinear SISO systems with respect to a real non-flat output is investigated in the coordinates of the flat output and its derivatives. The main result constitutes that the parameterization of the real output by the flat output and its derivatives up to a certain order forms a differential equation which is diffeomorphic to the aforementioned internal dynamics.