Differential–algebraic systems with dissipative Hamiltonian structure

Authors

Volker Mehrmann, Arjan van der Schaft

Abstract

Different representations of linear dissipative Hamiltonian and port-Hamiltonian differential–algebraic equations (DAE) systems are presented and compared. Using global geometric and algebraic points of view, translations between different representations are presented. Characterizations are also derived when a general DAE system can be transformed into one of these structured representations. Approaches for computing the structural information and the described transformations are derived that can be directly implemented as numerical methods. The results are demonstrated with a large number of examples.

Keywords

Port-Hamiltonian system; Dissipative Hamiltonian system; Differential–algebraic equation; Lagrange structure; Dirac structure; Matrix pencil

Citation

• Journal: Mathematics of Control, Signals, and Systems
• Year: 2023
• Volume: 35
• Issue: 3
• Pages: 541–584
• Publisher: Springer Science and Business Media LLC
• DOI: 10.1007/s00498-023-00349-2

BibTeX

@article{Mehrmann_2023,
  title={{Differential–algebraic systems with dissipative Hamiltonian structure}},
  volume={35},
  ISSN={1435-568X},
  DOI={10.1007/s00498-023-00349-2},
  number={3},
  journal={Mathematics of Control, Signals, and Systems},
  publisher={Springer Science and Business Media LLC},
  author={Mehrmann, Volker and van der Schaft, Arjan},
  year={2023},
  pages={541--584}
}

Download the bib file

References

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