The difference between port-Hamiltonian, passive and positive real descriptor systems

Authors

Karim Cherifi, Hannes Gernandt, Dorothea Hinsen

Abstract

The relation between passive and positive real systems has been extensively studied in the literature. In this paper, we study their connection to the more recently used notion of port-Hamiltonian descriptor systems. It is well-known that port-Hamiltonian systems are passive and that passive systems are positive real. Hence it is studied under which assumptions the converse implications hold. Furthermore, the relationship between passivity and KYP inequalities is investigated.

Keywords

Port-Hamiltonian systems; Differential-algebraic equations; Minimal realizations; Passive systems; Positive real systems; Kalman–Yakubovich–Popov inequality; Primary 34A09; 93C05; Secondary 93B20; 15A39

Citation

• Journal: Mathematics of Control, Signals, and Systems
• Year: 2024
• Volume: 36
• Issue: 2
• Pages: 451–482
• Publisher: Springer Science and Business Media LLC
• DOI: 10.1007/s00498-023-00373-2

BibTeX

@article{Cherifi_2023,
  title={{The difference between port-Hamiltonian, passive and positive real descriptor systems}},
  volume={36},
  ISSN={1435-568X},
  DOI={10.1007/s00498-023-00373-2},
  number={2},
  journal={Mathematics of Control, Signals, and Systems},
  publisher={Springer Science and Business Media LLC},
  author={Cherifi, Karim and Gernandt, Hannes and Hinsen, Dorothea},
  year={2023},
  pages={451--482}
}

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References

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