Parameterized Interpolation of Passive Systems

TL;DR

This paper introduces a new parameterized interpolation method for passive systems that enhances model robustness and accuracy by leveraging spectral zeros and deflating subspaces, applicable to both passive and certain non-passive systems.

Contribution

It presents novel interpolation conditions based on spectral zeros and deflating subspaces, improving low order model robustness and accuracy for passive and some non-passive systems.

Findings

Improved robustness of low order models.

New spectral zero selection procedure.

Applicable to non-passive systems with spectral zeros.

Abstract

We study the tangential interpolation problem for a passive transfer function in standard state-space form. We derive new interpolation conditions based on the computation of a deflating subspace associated with a selection of spectral zeros of a parameterized para-Hermitian transfer function. We show that this technique improves the robustness of the low order model and that it can also be applied to non-passive systems, provided they have sufficiently many spectral zeros in the open right half plane. We analyze the accuracy needed for the computation of the deflating subspace, in order to still have a passive lower order model and we derive a novel selection procedure of spectral zeros in order to obtain low order models with a small approximation error.