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

Port-Hamiltonian descriptor systems are relative generically controllable and stabilizable