Zero dynamics for waves on networks

Consider a network with linear dynamics on the edges, and observation and control in the nodes. Assume that on the edges there is no damping, and so the dynamics can be described by an infinite-dimensional, port-Hamiltonian system. For general infinite-dimensional systems, the zero dynamics can be difficult to characterize and are sometimes ill-posed. However, for this class of systems the zero dynamics are shown to be well-defined. Using the underlying structure, simple characterizations and a constructive procedure can be obtained.