Duality and singular value functions of the nonlinear normalized right and left coprime factorizations

This paper considers the nonlinear left coprime factorization (NLCF) of a nonlinear system. In order to study the balanced realization of such NLCF first a dual system notion is introduced. The important energy functions for the original NLCF and their relation with the dual NLCF are studied and relations between these functions are established. These developments can be used for studying a relation between the singular value functions of the NLCF and the normalized right coprime factorization (NRCF) of a nonlinear system. The singular value functions are a useful tool for model reduction of unstable nonlinear systems.