Structured Backward Errors for Eigenvalues of Linear Port-Hamiltonian Descriptor Systems

Authors

Volker Mehrmann, Paul Van Dooren

Abstract

When computing the eigenstructure of matrix pencils associated with the passivity analysis of perturbed port-Hamiltonian descriptor system using a structured generalized eigenvalue method, one should make sure that the computed spectrum satisfies the symmetries that corresponds to this structure and the underlying physical system. We perform a backward error analysis and show that for matrix pencils associated with port-Hamiltonian descriptor systems and a given computed eigenstructure with the correct symmetry structure there always exists a nearby port-Hamiltonian descriptor system with exactly that eigenstructure. We also derive bounds for how near this system is and show that the stability radius of the system plays a role in that bound.

Citation

• Journal: SIAM Journal on Matrix Analysis and Applications
• Year: 2021
• Volume: 42
• Issue: 1
• Pages: 1–16
• Publisher: Society for Industrial & Applied Mathematics (SIAM)
• DOI: 10.1137/20m1344184

BibTeX

@article{Mehrmann_2021,
  title={{Structured Backward Errors for Eigenvalues of Linear Port-Hamiltonian Descriptor Systems}},
  volume={42},
  ISSN={1095-7162},
  DOI={10.1137/20m1344184},
  number={1},
  journal={SIAM Journal on Matrix Analysis and Applications},
  publisher={Society for Industrial & Applied Mathematics (SIAM)},
  author={Mehrmann, Volker and Dooren, Paul Van},
  year={2021},
  pages={1--16}
}

Download the bib file

References

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