Optimal Robustness of Port-Hamiltonian Systems

Authors

Volker Mehrmann, Paul M. Van Dooren

Abstract

We construct optimally robust port-Hamiltonian realizations of a given rational transfer function that represents a passive system. We show that the realization with a maximal passivity radius is a normalized port-Hamiltonian one. Its computation is linked to a particular solution of a linear matrix inequality that defines passivity of the transfer function, and we provide an algorithm to construct this optimal solution. We also consider the problem of finding the nearest passive system to a given non-passive one and provide a simple but suboptimal solution.

Citation

• Journal: SIAM Journal on Matrix Analysis and Applications
• Year: 2020
• Volume: 41
• Issue: 1
• Pages: 134–151
• Publisher: Society for Industrial & Applied Mathematics (SIAM)
• DOI: 10.1137/19m1259092

BibTeX

@article{Mehrmann_2020,
  title={{Optimal Robustness of Port-Hamiltonian Systems}},
  volume={41},
  ISSN={1095-7162},
  DOI={10.1137/19m1259092},
  number={1},
  journal={SIAM Journal on Matrix Analysis and Applications},
  publisher={Society for Industrial & Applied Mathematics (SIAM)},
  author={Mehrmann, Volker and Van Dooren, Paul M.},
  year={2020},
  pages={134--151}
}

Download the bib file

References

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