A Kernel Representation of Dirac Structures for Infinite-dimensional Systems

Authors

O.V. Iftime, M. Roman, A. Sandovici

Abstract

Dirac structures are used as the underlying structure to mathematically formalize port-Hamiltonian systems. This note approaches the Dirac structures for infinite-dimensional systems using the theory of linear relations on Hilbert spaces. First, a kernel representation for a Dirac structure is proposed. The one-to-one correspondence between Dirac structures and unitary operators is revisited. Further, the proposed kernel representation and a scattering representation are constructively related. Several illustrative examples are also presented in the paper.

Citation

• Journal: Mathematical Modelling of Natural Phenomena
• Year: 2014
• Volume: 9
• Issue: 5
• Pages: 295–308
• Publisher: EDP Sciences
• DOI: 10.1051/mmnp/20149520

BibTeX

@article{Iftime_2014,
  title={{A Kernel Representation of Dirac Structures for Infinite-dimensional Systems}},
  volume={9},
  ISSN={1760-6101},
  DOI={10.1051/mmnp/20149520},
  number={5},
  journal={Mathematical Modelling of Natural Phenomena},
  publisher={EDP Sciences},
  author={Iftime, O.V. and Roman, M. and Sandovici, A.},
  editor={Damanik, David and Ruzhansky, Michael and Vougalter, Vitali and Wong, M.W.},
  year={2014},
  pages={295--308}
}

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