%0 Journal Article %1 BreU21 %A Breiten, Tobias %A Unger, Benjamin %D 2021 %J ArXiv e-print 2103.13194 %K EXC2075 from:benjaminunger myown pn4 preprint %T Passivity preserving model reduction via spectral factorization %U https://arxiv.org/abs/2103.13194 %X 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.

@article{BreU21, 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.}, added-at = {2021-12-08T17:10:08.000+0100}, author = {Breiten, Tobias and Unger, Benjamin}, biburl = {https://puma.ub.uni-stuttgart.de/bibtex/22ea9d8480d14574cdb42fdb97a34cab5/katharinafuchs}, interhash = {54147d320041de79c2c0f1093e0798fe}, intrahash = {2ea9d8480d14574cdb42fdb97a34cab5}, journal = {ArXiv e-print 2103.13194}, keywords = {EXC2075 from:benjaminunger myown pn4 preprint}, pubdate = {2021-03-25}, timestamp = {2021-12-08T16:10:08.000+0100}, title = {Passivity preserving model reduction via spectral factorization}, url = {https://arxiv.org/abs/2103.13194}, year = 2021 }