Asymptotic Stability of Port-Hamiltonian Systems

Authors

Abstract

We characterise asymptotic stability of port-Hamiltonian systems by means of matrix conditions using well-known resolvent criteria from C 0 \( \)C_0\( \) -semigroup theory. The idea of proof is based on a recent characterisation of exponential stability established in Trostorff and Waurick (Characterisation for Exponential Stability of port-Hamiltonian Systems, 2024), which was inspired by a structural observation concerning port-Hamiltonian systems from Picard et al. (SIAM J Control Optim 61(2):511–535, 2023). We apply the result to study the asymptotic stability of a network of vibrating strings.

Keywords

Port-Hamiltonian systems; Stability; -Semigroup; Infinite-dimensional systems theory

Citation

ISBN: 9783031649905
Publisher: Springer Nature Switzerland
DOI: 10.1007/978-3-031-64991-2_4
Note: Workshop on Systems Theory and PDEs

BibTeX

@inbook{Waurick_2024,
  title={{Asymptotic Stability of Port-Hamiltonian Systems}},
  ISBN={9783031649912},
  ISSN={2297-024X},
  DOI={10.1007/978-3-031-64991-2_4},
  booktitle={{Systems Theory and PDEs}},
  publisher={Springer Nature Switzerland},
  author={Waurick, Marcus and Zwart, Hans},
  year={2024},
  pages={91--122}
}

Download the bib file

References

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