On the equivalence of geometric and descriptor representations of linear port-Hamiltonian systems

We prove a one-to-one correspondence between the geometric formulation of port-Hamiltonian (pH) systems defined by Dirac structures, Lagrange structures, maximal resistive structures, and external ports and a state-space formulation by means of port-Hamiltonian descriptor systems, i.e., differential algebraic equations (DAE) with inputs and outputs.