Generic observability for port-Hamiltonian descriptor systems

Authors

Abstract

The present work is a successor of Ilchmann and Kirchhoff (Math Control Signals Syst 33:359–377, 2021. https://doi.org/10.1007/s00498-021-00287-x ), Ilchmann and Kirchhoff (Math Control Signals Syst 35:45–76, 2023. https://doi.org/10.1007/s00498-021-00287-x ) on (relative) generic controllability of unstructured linear differential-algebraic systems and of Ilchmann et al. (Port-Hamiltonian descriptor systems are generically controllable and stabilizable. Submitted to Mathematics of Control, Signals and Systems, 2023. https://arxiv.org/abs/2302.05156 ) on (relative) generic controllability of port-Hamiltonian descriptor systems. We extend their results to (relative) genericity of observability. For unstructured differential-algebraic systems, criteria for (relative) generic observability are derived from Ilchmann and Kirchhoff (Math Control Signals Syst 35:45–76, 2023. https://doi.org/10.1007/s00498-021-00287-x ) using duality. This is not possible for port-Hamiltonian systems. Hence, we tweak the results of Ilchmann et al. (Port-Hamiltonian descriptor systems are generically controllable and stabilizable. Submitted to Mathematics of Control, Signals and Systems, 2023. https://arxiv.org/abs/2302.05156 ) and derive similar criteria as for the unstructured case. Additionally, we consider certain rank constraints on the system matrices.

Keywords

Differential-algebraic equation; Port-Hamiltonian system; Controllability; Stabilizability; Genericity; Relative-genericity

Citation

Journal: Mathematics of Control, Signals, and Systems
Year: 2024
Volume: 36
Issue: 4
Pages: 831–873
Publisher: Springer Science and Business Media LLC
DOI: 10.1007/s00498-024-00388-3

BibTeX

@article{Kirchhoff_2024,
  title={{Generic observability for port-Hamiltonian descriptor systems}},
  volume={36},
  ISSN={1435-568X},
  DOI={10.1007/s00498-024-00388-3},
  number={4},
  journal={Mathematics of Control, Signals, and Systems},
  publisher={Springer Science and Business Media LLC},
  author={Kirchhoff, Jonas},
  year={2024},
  pages={831--873}
}

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References

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