  The class of port-Hamiltonian systems incorporates many physical models, such
as mechanical systems in the finite-dimensional case and wave and beam
equations in the infinite-dimensional case. In this paper we study a subclass
of linear first order port-Hamiltonian systems. These systems are exactly
observable when the energy is not dissipated internally and when sufficient
observations are made at the boundary. In this article we study the
observability properties for these systems when internal dissipation of energy
is possible. We cannot show the exact observability, but we do show that the
Hautus test is satisfied. In general, the Hautus test is weaker than exact
observability, but stronger than approximate observability. Hence we conclude
that these systems are approximately observable.
