Balancing relations between the normalized left and right coprime factorizations of a nonlinear system

This paper considers the relation between the singular value functions of the nonlinear normalized left coprime factorization (NLCF) and the nonlinear normalized right coprime factorization (NRCF). In previous work a new duality notion gave rise to a relation between the controllability, observability, future and past energy functions of the original system and its NLCF and NRCF. However, some linear parameter varying notions are still missing and are included in this paper. Both the NLCF and NRCF can be used for model reduction based on balanced realizations for an unstable nonlinear system. For linear systems model reduction based on balancing of the NLCF or NRCF yields the same reduced order model.