Interpolatory weighted-H2H2 model reduction

This paper introduces an interpolation framework for the weighted-H2H2 model reduction problem. We obtain a new representation of the weighted-H2H2 norm of SISO systems that provides new interpolatory first order necessary conditions for an optimal reduced-order model. The H2H2 norm representation also provides an error expression that motivates a new weighted-H2H2 model reduction algorithm. Several numerical examples illustrate the effectiveness of the proposed approach.