Model reduction by moment matching for ZIP systems

The family of linear systems satisfying the “zeros-interlacing-poles” (ZIP) property is considered. For these systems the problem of model reduction by moment matching is investigated. It is shown that, under some assumptions, the ZIP property is preserved by the reduced order model. The problem of determining ZIP reduced order models with prescribed eigenvalues is studied and necessary and sufficient conditions for the solution of the eigenvalue placement problem are provided. Polynomial and graphical interpretations of such conditions are also given.