Local and Global Canonical Forms for Differential-Algebraic Equations with Symmetries

Authors

Peter Kunkel, Volker Mehrmann

Abstract

Linear time-varying differential-algebraic equations with symmetries are studied. The structures that we address are self-adjoint and skew-adjoint systems. Local and global canonical forms under congruence are presented and used to classify the geometric properties of the flow associated with the differential equation as symplectic or generalized orthogonal flow. As applications, the results are applied to the analysis of dissipative Hamiltonian systems arising from circuit simulation and incompressible flow.

Keywords

Differential-algebraic equation; Self-adjoint system; Skew-adjoint system; Dissipative Hamiltonian system; Canonical form under congruence; 37J05; 65L80; 65L05; 65P10; 49K15

Citation

• Journal: Vietnam Journal of Mathematics
• Year: 2023
• Volume: 51
• Issue: 1
• Pages: 177–198
• Publisher: Springer Science and Business Media LLC
• DOI: 10.1007/s10013-022-00596-x

BibTeX

@article{Kunkel_2022,
  title={{Local and Global Canonical Forms for Differential-Algebraic Equations with Symmetries}},
  volume={51},
  ISSN={2305-2228},
  DOI={10.1007/s10013-022-00596-x},
  number={1},
  journal={Vietnam Journal of Mathematics},
  publisher={Springer Science and Business Media LLC},
  author={Kunkel, Peter and Mehrmann, Volker},
  year={2022},
  pages={177--198}
}

Download the bib file

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