Passivity preserving model reduction via spectral factorization

TL;DR

This paper introduces a passivity-preserving model reduction technique for linear systems using spectral factorization, enabling efficient large-scale structure-preserving reduction with high fidelity.

Contribution

It develops a novel MOR method based on spectral factorization that maintains passivity and exploits sparsity, improving large-scale pH system reduction.

Findings

Produces high-fidelity reduced models close to $\\mathcal{H}_2$-optimal models.

Enables MOR directly on spectral factors, preserving system structure.

Beneficial for large-scale port-Hamiltonian system reduction.

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.