Linear port-Hamiltonian DAE systems revisited

TL;DR

This paper extends the theory of port-Hamiltonian differential-algebraic equations (DAEs) by exploring their structure through maximally monotone spaces, providing new representations and transfer functions for multi-physics system modeling.

Contribution

It introduces a novel framework for representing port-Hamiltonian DAE systems using maximally monotone structures, building on recent theoretical advancements.

Findings

Any maximally monotone space can be decomposed into Dirac and resistive structures.

Provides explicit coordinate representations for these systems.

Derives explicit transfer functions for the extended port-Hamiltonian DAE models.

Abstract

Port-Hamiltonian systems theory provides a systematic methodology for the modeling, simulation and control of multi-physics systems. The incorporation of algebraic constraints has led to a multitude of definitions of port-Hamiltonian differential-algebraic equations (DAE) systems. This paper presents extensions of results in Gernandt, Haller & Reis (2021) and Mehrmann & Van der Schaft (2022) in the context of maximally monotone structures and shows that any such space can be written as composition of a Dirac and a resistive structure. Furthermore, appropriate coordinate representations are presented as well as explicit expressions for the associated transfer functions.