Dirac structure for linear dynamical systems on Sobolev spaces

The port-Hamiltonian structure of linear dynamical systems is defined by a Dirac structure. In this paper we prove existence and well-posedness of a Dirac structure for linear dynamical systems on Sobolev spaces of differential forms on a bounded, connected and oriented manifold with Lipschitz continuous boundary. This result extends the proof of a Dirac structure for linear dynamical systems originally defined on smooth differential forms to a much larger class of function spaces, which is of theoretical importance and provides a solid basis for the numerical discretization of many linear port-Hamiltonian dynamical systems.