Passivity preserving model reduction via spectral factorization
Abstract
We present a novel modelorder reduction (MOR) method for linear timeinvariant systems that preserves passivity and is thus suited for structurepreserving MOR for portHamiltonian (pH) systems. Our algorithm exploits the wellknown spectral factorization of the Popov function by a solution of the KalmanYakubovichPopov (KYP) inequality. It performs MOR directly on the spectral factor inheriting the original system's sparsity enabling MOR in a largescale 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 pHpreserving MOR methods such as a modified version of the iterative rational Krylov algorithm (IRKA). Numerical examples demonstrate that our approach can produce highfidelity reducedorder models close to (unstructured) $\mathcal{H}_2$optimal reducedorder models.
 Publication:

arXiv eprints
 Pub Date:
 March 2021
 arXiv:
 arXiv:2103.13194
 Bibcode:
 2021arXiv210313194B
 Keywords:

 Mathematics  Dynamical Systems;
 Mathematics  Numerical Analysis;
 30E05;
 37M99;
 65P99;
 93A30;
 93A15;
 93B99