Weighted Model Reduction Via Interpolation

Weighted model reduction problems appear in many important applications such as controller reduction. The most common approach to this problem is the weighted balanced truncation method. Interpolatory approaches to weighted model reduction have been mostly limited to simply choosing interpolation points in the regions where the weights are dominant. In this paper, we extend the (unweighted) tangential interpolatory model reduction to the weighted case using the recent generalized interpolation framework of Beattie and Gugercin [2009]. We generate a reduced-order model such that the weighted reduced-order system tangentially interpolates the weighted full-order system at the provided interpolation data.