Identity Between Bounded Real and Positive Real Characteristic Values Through the Scattering Relation

In this paper, new results regarding the identity that occurs between the characteristic values of the scattering matrix S(s) and the characteristic values of the corresponding impedance matrix Z(s) are provided. The results allow us to obtain reduced-order models with similar approximation degree, considering both the approximation of S(s) and of the model Z(s). Even if the computation of the impedance matrix is more immediate, in many cases, the scattering systems S(s) are considered; therefore, in order to avoid different information degradation between the two reduced-order systems, they must be consistent. Numerical examples regarding both electrical networks and multi-port mechanical systems are discussed.