Riesz Bases of Port-Hamiltonian Systems

Authors

Birgit Jacob, Julia T. Kaiser, Hans Zwart

Abstract

The location of the spectrum and the Riesz basis property of well-posed homogeneous infinite-dimensional linear port-Hamiltonian systems on a 1D spatial domain are studied. It is shown that the Riesz basis property is equivalent to the fact that system operator generates a strongly continuous group. Moreover, in this situation the spectrum consists of eigenvalues only, located in a strip parallel to the imaginary axis and they can decomposed into finitely many sets having each a uniform gap.

Citation

Journal: SIAM Journal on Control and Optimization
Year: 2021
Volume: 59
Issue: 6
Pages: 4646–4665
Publisher: Society for Industrial & Applied Mathematics (SIAM)
DOI: 10.1137/20m1366216

BibTeX

@article{Jacob_2021,
  title={{Riesz Bases of Port-Hamiltonian Systems}},
  volume={59},
  ISSN={1095-7138},
  DOI={10.1137/20m1366216},
  number={6},
  journal={SIAM Journal on Control and Optimization},
  publisher={Society for Industrial & Applied Mathematics (SIAM)},
  author={Jacob, Birgit and Kaiser, Julia T. and Zwart, Hans},
  year={2021},
  pages={4646--4665}
}

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References

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