Balanced Order Reduction for Nonlinear Systems; Duality and Normalized Coprime Factorizations

In this presentation, first a brief overview about the previous recent results on balanced realizations for stable nonlinear systems will be given. Then, a new definition of singular value functions will be taken to study balanced realizations for unstable nonlinear systems by balancing the normalized coprime factorizations. The relation between the singular value functions of the nonlinear normalized left coprime factorization (NLCF) and the nonlinear normalized right coprime factorization (NRCF) will be studied. 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. 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. In this study, model reduction based on the balanced realization of the NLCF and NRCF of a nonlinear system is compared and relations are found.

Jacquelien Scherpen, University of Groningen, The Netherlands

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