On the stability of port-Hamiltonian descriptor systems

Authors

Hannes Gernandt, Frédéric E. Haller

Abstract

We characterize stable differential-algebraic equations (DAEs) using a generalized Lyapunov inequality. The solution of this inequality is then used to rewrite stable DAEs as dissipative Hamiltonian (dH) DAEs on the subspace where the solutions evolve. Conversely, we give sufficient conditions guaranteeing stability of dH DAEs. Further, for stabilizable descriptor systems we construct solutions of generalized algebraic Bernoulli equations which can then be used to rewrite these systems as pH descriptor systems. Furthermore, we show how to describe the stable and stabilizable systems using Dirac and Lagrange structures.

Keywords

Descriptor systems; port-Hamiltonian systems; stability; differential-algebraic equations; linear matrix inequalities; Dirac structure

Citation

• Journal: IFAC-PapersOnLine
• Year: 2021
• Volume: 54
• Issue: 19
• Pages: 137–142
• Publisher: Elsevier BV
• DOI: 10.1016/j.ifacol.2021.11.068
• Note: 7th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC 2021- Berlin, Germany, 11-13 October 2021

BibTeX

@article{Gernandt_2021,
  title={{On the stability of port-Hamiltonian descriptor systems}},
  volume={54},
  ISSN={2405-8963},
  DOI={10.1016/j.ifacol.2021.11.068},
  number={19},
  journal={IFAC-PapersOnLine},
  publisher={Elsevier BV},
  author={Gernandt, Hannes and Haller, Frédéric E.},
  year={2021},
  pages={137--142}
}

Download the bib file

References

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