Dirac structure for linear dynamical systems on Sobolev spaces

Authors

N. Kumar, H.J. Zwart, J.J.W. van der Vegt

Abstract

The port-Hamiltonian structure of linear dynamical systems is defined by a Dirac structure. In this paper we prove existence and well-posedness of a Dirac structure for linear dynamical systems on Sobolev spaces of differential forms on a bounded, connected and oriented manifold with Lipschitz continuous boundary. This result extends the proof of a Dirac structure for linear dynamical systems originally defined on smooth differential forms to a much larger class of function spaces, which is of theoretical importance and provides a solid basis for the numerical discretization of many linear port-Hamiltonian dynamical systems.

Keywords

Port-Hamiltonian systems; Dirac structure; Sobolev spaces of differential forms

Citation

• Journal: Journal of Mathematical Analysis and Applications
• Year: 2025
• Volume: 549
• Issue: 2
• Pages: 129493
• Publisher: Elsevier BV
• DOI: 10.1016/j.jmaa.2025.129493

BibTeX

@article{Kumar_2025,
  title={{Dirac structure for linear dynamical systems on Sobolev spaces}},
  volume={549},
  ISSN={0022-247X},
  DOI={10.1016/j.jmaa.2025.129493},
  number={2},
  journal={Journal of Mathematical Analysis and Applications},
  publisher={Elsevier BV},
  author={Kumar, N. and Zwart, H.J. and van der Vegt, J.J.W.},
  year={2025},
  pages={129493}
}

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