A new result on passivity preserving model reduction

The problem of model reduction with preservation of passivity is investigated. The approach is based on positive real interpolation, and is inspired by the similarity between Löwner and Pick matrices. The former are important in problems of general rational interpolation while the latter in problems of interpolation by positive real functions. It follows that interpolation of the original set of data together with an appropriately defined mirror-image set of data yields automatically positive real interpolants. Subsequently, we show how this result can be implemented using a Krylov projection procedure. The ensuing model reduction method preserves stability and passivity and can be implemented efficiently for the large-scale systems.