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) $\mathcal{H}_2$-optimal reduced-order models.
- Publication:
-
arXiv e-prints
- Pub Date:
- March 2021
- DOI:
- 10.48550/arXiv.2103.13194
- arXiv:
- arXiv:2103.13194
- Bibcode:
- 2021arXiv210313194B
- Keywords:
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- Mathematics - Dynamical Systems;
- Mathematics - Numerical Analysis;
- 30E05;
- 37M99;
- 65P99;
- 93A30;
- 93A15;
- 93B99