A parametrization for closed-loop identification of nonlinear systems based on differentially coprime kernel representations

In this paper, we use the notion of a differentially coprime kernel represe ntation to parametrize the set of all nonlinear plants stabilized by a give n nonlinear controller using a so-called Youla parameter and to unify under standing of some stability concepts for nonlinear systems. By utilizing the differential kernel representation concept, we are able to convert a close d-loop identification problem into one of open-loop identification. The mai n advantage of our approach using kernel representations over fractional de scriptions is that we address a larger class of nonlinear systems. The idea of a differential kernel representation allows us also to clarify the rela tionship between three different notions of internal stability available in the literature. The results in the paper thus provide new insights to the stability of nonlinear feedback systems. (C) 2001 Elsevier Science Ltd. All rights reserved.