On Representations of Linear Port-Hamiltonian Systems defined by Dirac and Lagrange structures

Authors

Javier Caballeria, Hector Ramirez, Laurent Lefèvre, Yann Le Gorrec

Abstract

Linear port-Hamiltonian systems (PHS) defined by Dirac and Lagrange structures, referred to as port-Hamiltonian differential-algebraic equation systems (PH DAEs), incorporate a class of algebraic constraints arising from energy deficiency in the Hamiltonian definition, known as Lagrange algebraic constraints. This paper presents two novel equivalent characterizations of linear PH DAEs with Lagrange constraints, including resistive and external ports. Relations to constrained input-output PHS formulations are established. The constraints are shown to be transferable between Dirac and Lagrange structures, enabling equivalent representations in terms of state or effort variables. The proposed formulations are illustrated using a micro-robotic contact scenario model.

Keywords

algebraic constraints, differential-algebraic equations systems, lagrange and dirac structure, port-hamiltonian systems

Citation

• Journal: IFAC-PapersOnLine
• Year: 2026
• Volume: 60
• Issue: 1
• Pages: 115–120
• Publisher: Elsevier BV
• DOI: 10.1016/j.ifacol.2026.09.020
• Note: 27th International Symposium on Mathematical Theory of Networks and Systems MTNS 2026- Waterloo, Ontario, August 17-21, 2026

BibTeX

@article{Caballeria_2026,
  title={{On Representations of Linear Port-Hamiltonian Systems defined by Dirac and Lagrange structures}},
  volume={60},
  ISSN={2405-8963},
  DOI={10.1016/j.ifacol.2026.09.020},
  number={1},
  journal={IFAC-PapersOnLine},
  publisher={Elsevier BV},
  author={Caballeria, Javier and Ramirez, Hector and Lefèvre, Laurent and Gorrec, Yann Le},
  year={2026},
  pages={115--120}
}

Download the bib file

References

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