Projection-Based Model Reduction for Time-Varying Descriptor Systems Using Recycled Krylov Subspaces

We will present a projection approach for model reduction of linear time-varying descriptor systems based on earlier ideas in the work of Philips and others. 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 macromodels, such as time varying circuit systems and models arising in network interconnection, on limited frequency ranges. Bode plots and step response are used to illustrate the performance of the reduced order models.