A Linear Relation Approach to Port-Hamiltonian Differential-Algebraic Equations

Abstract

We consider linear port-Hamiltonian differential-algebraic equations. Inspired by the geometric approach of van der Schaft and Maschke [System Control Lett., 121 (2018), pp. 31--37] and the linear algebraic approach of Mehl, Mehrmann, and Wojtylak [SIAM J. Matrix Anal. Appl., 39 (2018), pp. 1489--1519], we present another view by using the theory of linear relations. We show that this allows us 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.