Projection-based model reduction for time-varying descriptor systems : new results / Mohammad-Sahadet Hossain, Peter Benner

Abstract

Abstract: We have presented a projection-based approach for model reduction of linear time-varying descriptor systems in [Hossain et. at. \'08] which was based on earlier ideas in the work of J. Philips [Phillips\'98] and others. This contribution continues that work by presenting more details of linear time-varying descriptor systems and new results coming from real fields of application. The idea behind the proposed procedure is based on a multipoint rational approximation of the monodromy matrix of the corresponding differential-algebraic equation. This is realized by orthogonal projection onto a rational Krylov subspace. The algorithmic realization of the method employs recycling techniques for shifted Krylov subspaces and their invariance properties. The proposed method works efficiently for macro-models, such as time varying circuit systems and models arising in network interconnection. Bode plots and step response are used to illustrate both the stability and accuracy of the reduced order models.