Structure Preserving Moment Matching for Port-Hamiltonian Systems: Arnoldi and Lanczos

Authors

Rostyslav V. Polyuga, Arjan van der Schaft

Abstract

Structure preserving model reduction of single-input single-output port-Hamiltonian systems is considered by employing the rational Krylov methods. The rational Arnoldi method is shown to preserve (for the reduced order model) not only a specific number of the moments at an arbitrary point in the complex plane but also the port-Hamiltonian structure. Furthermore, it is shown how the rational Lanczos method applied to a subclass of port-Hamiltonian systems, characterized by an algebraic condition, preserves the port-Hamiltonian structure. In fact, for the same subclass of port-Hamiltonian systems the rational Arnoldi method and the rational Lanczos method turn out to be equivalent in the sense of producing reduced order port-Hamiltonian models with the same transfer function.

Citation

• Journal: IEEE Transactions on Automatic Control
• Year: 2011
• Volume: 56
• Issue: 6
• Pages: 1458–1462
• Publisher: Institute of Electrical and Electronics Engineers (IEEE)
• DOI: 10.1109/tac.2011.2128650

BibTeX

@article{Polyuga_2011,
  title={{Structure Preserving Moment Matching for Port-Hamiltonian Systems: Arnoldi and Lanczos}},
  volume={56},
  ISSN={0018-9286},
  DOI={10.1109/tac.2011.2128650},
  number={6},
  journal={IEEE Transactions on Automatic Control},
  publisher={Institute of Electrical and Electronics Engineers (IEEE)},
  author={Polyuga, Rostyslav V. and van der Schaft, Arjan},
  year={2011},
  pages={1458--1462}
}

Download the bib file

References

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