From Characteristic Values of PR‐Inverse Systems to Model Order Reduction

ABSTRACT In this note, a new result is proved: the inverse of a positive real (PR) system has the same characteristic values as the original system. Specifically, given a proper impedance transfer function matrix , its corresponding admittance transfer function matrix shares the same characteristic values. This observation enables the derivation of approximated models of the same order for both and . Moreover, by considering a system of order , if the truncated models and its inverse are constructed based on the characteristic values and a balancing procedure involving the PR Riccati equation, then the error bounds for both models are governed by the same quantity, which depends on the discarded characteristic values . A significant numerical example referring to an extended RLC cascade system is presented, along with the procedure to obtain the PR Riccati‐based balanced representation, which is provided at the end of the paper.