A structural observation on port-hamiltonian systems

We study port-Hamiltonian systems on a family of intervals and characterize all boundary conditions leading to m-accretive realizations of the port-Hamiltonian operator and thus to generators of contractive semigroups. The proofs are based on a structural observation that the port-Hamiltonian operator can be transformed to the derivative on a familiy of reference intervals by suitable congruence relations, allowing for studying the simpler case of a transport equation. Moreover, we provide well-posedness results for associated control problems without assuming any additional regularity of the operators involved.