Beschreibung:
We present a framework to formulate infinite dimensional port-Hamiltonian systems by means of system nodes, which provide a very general and powerful setting for unbounded input and output operators that appear, e.g., in the context of boundary control or observation. One novelty of our approach is that we allow for unbounded and not necessarily coercive Hamiltonian energies. To this end, we construct finite energy spaces to define the port-Hamiltonian dynamics and give an application in case of multiplication operator Hamiltonians where the Hamiltonian density does not need to be positive or bounded. In order to model systems involving differential operators on these finite energy spaces, we show that if the total mass w.r.t. the Hamiltonian density (and its inverse) is finite, one can define a unique weak derivative.