Interpolatory Weighted-H2 Model Reduction

TL;DR

This paper presents a novel interpolation-based framework for weighted-H2 model reduction, offering new optimality conditions, an error expression, and an effective reduction algorithm demonstrated through numerical examples.

Contribution

It introduces a new interpolatory approach for weighted-H2 model reduction, including a novel norm representation and necessary conditions for optimality.

Findings

The new representation of the weighted-H2 norm facilitates the derivation of optimality conditions.

The proposed algorithm effectively reduces models as shown in numerical examples.

The approach improves upon existing methods in weighted-H2 model reduction.

Abstract

This paper introduces an interpolation framework for the weighted-H2 model reduction problem. We obtain a new representation of the weighted-H2 norm of SISO systems that provides new interpolatory first order necessary conditions for an optimal reduced-order model. The H2 norm representation also provides an error expression that motivates a new weighted-H2 model reduction algorithm. Several numerical examples illustrate the effectiveness of the proposed approach.