Stable kernel representations as nonlinear left coprime factorizations

A representation of nonlinear systems based on the idea of representing the input-output pairs of the system as elements of the kernel of a stable operator has been previously introduced by the authors (1993, 1994). This has been denoted the kernel representation of the system. In this paper it is demonstrated that the kernel representation is a generalization of the left coprime factorization of a general nonlinear system in the sense that it is a dual operator to the right coprime factorization of a nonlinear system. The results obtainable in the linear case linking left and right coprime factorizations are shown to be reproduced within the kernel representation framework