Passivity-preserving model reduction by analytic interpolation
2007 (English)In: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 425, no 2-3, 608-633 p.Article in journal (Refereed) Published
Antoulas and Sorensen have recently proposed a passivity-preserving model-reduction method of linear systems based on Krylov projections. The idea is to approximate a positive-real rational transfer function with one of lower degree. The method is based on an observation by Antoulas (in the single-input/single-output case) that if the approximant is preserving a subset of the spectral zeros and takes the same values as the original transfer function in the mirror points of the preserved spectral zeros, then the approximant is also positive real. However, this turns out to be a special solution in the theory of analytic interpolation with degree constraint developed by Byrnes, Georgiou and Lindquist, namely the maximum-entropy (central) solution. By tuning the interpolation points and the spectral zeros, as prescribed by this theory, one is able to obtain considerably better reduced-order models. We also show that, in the multi-input/multi-output case, Sorensen's algorithm actually amounts to tangential Nevanlinna-Pick interpolation.
Place, publisher, year, edition, pages
2007. Vol. 425, no 2-3, 608-633 p.
model reduction, passivity, interpolation, spectral zeros, positive-real functions, rational approximation
IdentifiersURN: urn:nbn:se:kth:diva-14157DOI: 10.1016/j.laa.2007.03.014ISI: 000249065400021ScopusID: 2-s2.0-34447551585OAI: oai:DiVA.org:kth-14157DiVA: diva2:331019
QC 201007212010-07-202010-07-202010-07-21Bibliographically approved