A linear relation approach to port-Hamiltonian differential-algebraic equations

TL;DR

This paper introduces a novel perspective on linear port-Hamiltonian differential-algebraic equations (pH-DAEs) by employing linear relations, bridging geometric and algebraic approaches, and analyzing associated matrix pencils.

Contribution

It presents a new framework using linear relations to unify geometric and algebraic views of pH-DAEs and studies the properties of related matrix pencils.

Findings

Unified class of DAEs combining geometric and algebraic approaches

Analysis of matrix pencils arising from the linear relations framework

Enhanced understanding of properties of pH-DAEs

Abstract

We consider linear port-Hamiltonian differential-algebraic equations (pH-DAEs). Inspired by the geometric approach of Maschke and van der Schaft and the linear algebraic approach of Mehl, Mehrmann and Wojtylak, we present another view by using the theory of linear relations. We show that this allows to elaborate the differences and mutualities of the geometric and linear algebraic views, and we introduce a class of DAEs which comprises these two approaches. We further study the properties of matrix pencils arising from our approach via linear relations.