Linear port-Hamiltonian DAE systems revisited

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 in the literature. This paper presents extensions of results obtained in Gernandt et al. (2021); Mehrmann and van der Schaft (2023) in the context of maximally monotone structures, and shows that any such structure can be written as the composition of a Dirac and a resistive structure. This yields an alternative, but equivalent, definition of linear port-Hamiltonian DAE systems with certain advantages. In particular, it leads to simpler coordinate representations, as well as to explicit expressions for the associated transfer functions.