  The structure preserving stabilization of (possibly non-regular) linear
port-Hamiltonian descriptor (pHDAE) systems by output feedback is discussed.
While for general descriptor systems the characterization when there exist
output feedbacks that lead to an asymptotically stable closed loop system is a
very hard and partially open problem, for systems in pHDAE representation this
problem can be completely solved. Necessary and sufficient conditions are
presented that guarantee that there exist a proportional output feedback such
that the resulting closed-loop port-Hamiltonian descriptor system is (robustly)
asymptotically stable. For this it is also necessary that the output feedback
also makes the problem regular and of index at most one. A complete
characterization when this is possible is presented as well.
