Passivity preserving model reduction via spectral factorization
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) -optimal reduced-order models.
Cite
@article{arxiv.2103.13194,
title = {Passivity preserving model reduction via spectral factorization},
author = {Tobias Breiten and Benjamin Unger},
journal= {arXiv preprint arXiv:2103.13194},
year = {2021}
}