Relationship between dissipativity concepts for linear time-varying port-Hamiltonian systems

Authors

Karim Cherifi, Hannes Gernandt, Dorothea Hinsen, Volker Mehrmann, Riccardo Morandin

Abstract

The relationship between different dissipativity concepts for linear time-varying systems is studied, in particular between port-Hamiltonian systems, passive systems, and systems with nonnegative supply. It is shown that linear time-varying port-Hamiltonian systems are passive, have nonnegative supply rates, and solve (under different smoothness assumptions) Kalman–Yakubovich–Popov differential and integral inequalities. The converse relations are also studied in detail. In particular, sufficient conditions are presented to obtain a port-Hamiltonian representation starting from any of the other dissipativity concepts. Two applications are presented.

Keywords

Port-Hamiltonian system; Passivity; Nonnegativity; Kalman–Yakubovich–Popov inequality; System transformation; 93A30; 65L80; 93B17; 93B11

Citation

• Journal: Mathematics of Control, Signals, and Systems
• Year: 2025
• Volume:
• Issue:
• Pages:
• Publisher: Springer Science and Business Media LLC
• DOI: 10.1007/s00498-025-00421-z

BibTeX

@article{Cherifi_2025,
  title={{Relationship between dissipativity concepts for linear time-varying port-Hamiltonian systems}},
  ISSN={1435-568X},
  DOI={10.1007/s00498-025-00421-z},
  journal={Mathematics of Control, Signals, and Systems},
  publisher={Springer Science and Business Media LLC},
  author={Cherifi, Karim and Gernandt, Hannes and Hinsen, Dorothea and Mehrmann, Volker and Morandin, Riccardo},
  year={2025}
}

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