Weighted balanced truncation for unstable nonlinear systems using coprime factorizations

This paper is concerned with a weighted model order reduction method for unstable nonlinear systems. Since balanced truncation method is only applicable to asymptotically stable systems, this method is applied to a coprime factorization of the original model and then the reduced order model of the coprime factorization derives that of the original model. This paper discusses how to construct coprime factorizations in such a way that the coprimeness is preserved under the model reduction procedure. This analysis prevents one from obtaining a reduced order model with unstable pole/zero cancellations. Furthermore, numerical simulations demonstrate the effectiveness of the proposed method