Solving high‐dimensional Lyapunov inequalities to obtain linear port‐Hamiltonian systems

Authors

Abstract

We investigate high‐dimensional linear dynamical systems. Each system can be converted into a port‐Hamiltonian formulation. A positive definite transformation matrix has to be identified, which satisfies a Lyapunov inequality. We apply a recent approach for the approximate solution of high‐dimensional Lyapunov equations, which guarantees the positive definiteness of an approximation. Results of numerical computations are presented using a benchmark.

Citation

Journal: PAMM
Year: 2018
Volume: 18
Issue: 1
Pages:
Publisher: Wiley
DOI: 10.1002/pamm.201800205

BibTeX

@article{Pulch_2018,
  title={{Solving high‐dimensional Lyapunov inequalities to obtain linear port‐Hamiltonian systems}},
  volume={18},
  ISSN={1617-7061},
  DOI={10.1002/pamm.201800205},
  number={1},
  journal={PAMM},
  publisher={Wiley},
  author={Pulch, Roland},
  year={2018}
}

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References

Beattie, C. A., Mehrmann, V. & Van Dooren, P. Robust port-Hamiltonian representations of passive systems. Automatica 100, 182–186 (2019) – 10.1016/j.automatica.2018.11.013
Wachspress, E. L. Trail to a Lyapunov equation solver. Computers & Mathematics with Applications 55, 1653–1659 (2008) – 10.1016/j.camwa.2007.04.048
Wolf, T., Lohmann, B., Eid, R. & Kotyczka, P. Passivity and Structure Preserving Order Reduction of Linear Port-Hamiltonian Systems Using Krylov Subspaces. European Journal of Control 16, 401–406 (2010) – 10.3166/ejc.16.401-406
Jacob, B. & Zwart, H. J. Homogeneous Port-Hamiltonian Systems. Linear Port-Hamiltonian Systems on Infinite-dimensional Spaces 79–96 (2012) doi:10.1007/978-3-0348-0399-1_7 – 10.1007/978-3-0348-0399-1_7