A Rosenbrock framework for tangential interpolation of port-Hamiltonian descriptor systems

TL;DR

This paper introduces a structure-preserving model order reduction framework for large-scale port-Hamiltonian descriptor systems, leveraging Rosenbrock system matrices to produce minimal, interpolating reduced models that maintain system properties.

Contribution

The method exploits Rosenbrock system matrix structures to generate minimal, tangentially interpolating reduced models that preserve port-Hamiltonian form, enabling safe coupling in large system networks.

Findings

Produces reduced models of minimal dimension

Ensures reduced models are in port-Hamiltonian form

Facilitates safe coupling with other systems

Abstract

We present a new structure-preserving model order reduction (MOR) framework for large-scale port-Hamiltonian descriptor systems (pH-DAEs). Our method exploits the structural properties of the Rosenbrock system matrix for this system class and utilizes condensed forms which often arise in applications and reveal the solution behaviour of a system. Provided that the original system has such a form, our method produces reduced-order models (ROMs) of minimal dimension, which tangentially interpolate the original model's transfer function and are guaranteed to be again in pH-DAE form. This allows the ROM to be safely coupled with other dynamical systems when modelling large system networks, which is useful, for instance, in electric circuit simulation.