  The present work is a successor of [Ilchmann, Kirchhoff 2022] on generic
controllability and of [Ilchmann, Kirchhoff 2023] on relative generic
controllability of linear differential-algebraic equations. We extend the
result from general, unstructured differential-algebraic equations to
differential-algebraic equations of port-Hamiltonian type. We derive new
results on relative genericity. These findings are the basis for characterizing
relative generic controllability of port-Hamiltonian systems in terms of
dimensions. A similar result is proved for relative generic stabilizability.
