Port-Hamiltonian Realizations of Positive Real Descriptor Systems
<|reference_start|>Port-Hamiltonian Realizations of Positive Real Descriptor Systems: The relationship between port-Hamiltonian and positive real descriptor systems is investigated. It is well-known that port-Hamiltonian systems are positive real, but the converse implication does not always hold. In [K. Cherifi, H. Gernandt, and D. Hinsen. The difference between port-Hamiltonian, passive and positive real descriptor systems. Math. Control Signals Systems, pages 1-32, 2023] sufficient conditions for the converse are presented. We refine these conditions and present for a completely controllable, completely observable and positive real descriptor system a necessary and sufficient condition as well as an explicit method to compute a port-Hamiltonian realization of a general positive real descriptor system.<|reference_end|>
@article{chu2024port-hamiltonian,
    title={Port-Hamiltonian Realizations of Positive Real Descriptor Systems},
    author={Delin Chu and Volker Mehrmann},
    journal={arXiv preprint arXiv:2408.14115},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.14115},
    primaryClass={math.OC cs.NA math.NA}
}