Parametrization of all internally stabilizing plant and controller pairs via differentially coprime kernel representations

In this paper, we use the notion of a differentially coprime kernel representation to parametrize the set of all internally stabilizing nonlinear plant and controller pairs using a so called Youla parameter and to unify understanding of some stability concepts for nonlinear systems. The idea of a differential kernel representation allows us to clarify the relationship between three different notions of internal stability available in the literature. Furthermore the parametrization derived here is applicable to nonlinear closed-loop indentification problems.