Time Domain Model Reduction by Moment Matching

Abstract

This dissertation delivers new results in the model reduction of large-scale linear timeinvariant dynamical systems.In particular, it suggests solutions for the well-known problem of finding a suitable interpolation point in order reduction by moment matching.As a first step, a new time-domain model order reduction method based on matching some of the first Laguerre coefficients of the impulse response is presented.Then, the equivalence between the classical moment matching and the Laguerre-based reduction approaches both in time-and frequency-domain is shown.In addition, this equivalence is generalized to include a larger family of coefficients known as generalized Markov parameters.This allows a first time-domain interpretation of the moment matching approach which has been until now developed and applied only in the frequency domain.Moreover, using this equivalence, the open problem of choosing an optimal expansion point in the rational Krylov subspace reduction methods (moment matching about s 0 = 0) is reformulated to the problem of finding the optimal parameter in the Laguerrebased reduction methods.Based on the Laguerre representation of the system, two methods for the choice of the Laguerre parameter and, consequently, the single expansion point in rational interpolation order reduction are presented.Accordingly, different model reduction algorithms are suggested.The importance of these approaches lies in the fact that they try to approximate the impulse response of the original system, have a simple structure, are numerically efficient, and are suitable for the reduction of large-scale systems.To my family and my wife.