Authors

Tobias Breiten, Benjamin Unger

Abstract

We present a novel model-order reduction (MOR) method for linear time-invariant systems that preserves passivity and is thus suited for structure-preserving MOR for port-Hamiltonian (pH) systems. Our algorithm exploits the well-known spectral factorization of the Popov function by a solution of the Kalman–Yakubovich–Popov (KYP) inequality. It performs MOR directly on the spectral factor inheriting the original system’s sparsity enabling MOR in a large-scale context. Our analysis reveals that the spectral factorization corresponding to the minimal solution of an associated algebraic Riccati equation is preferable from a model reduction perspective and benefits pH-preserving MOR methods such as a modified version of the iterative rational Krylov algorithm (IRKA). Numerical examples demonstrate that our approach can produce high-fidelity reduced-order models close to (unstructured) H 2 -optimal reduced-order models.

Keywords

Port-Hamiltonian systems; Structure-preserving model-order reduction; Passivity; Spectral factorization; \( H^2 \)-optimal

Citation

BibTeX

@article{Breiten_2022,
  title={{Passivity preserving model reduction via spectral factorization}},
  volume={142},
  ISSN={0005-1098},
  DOI={10.1016/j.automatica.2022.110368},
  journal={Automatica},
  publisher={Elsevier BV},
  author={Breiten, Tobias and Unger, Benjamin},
  year={2022},
  pages={110368}
}

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References