New Algorithms for Polynomial J-Spectral Factorization |
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Authors: | Harry L. Trentelman Paolo Rapisarda |
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Affiliation: | (1) Research Institute for Mathematics and Computing Science, P.O. Box 800, 9700 AV Groningen, The Netherlands. H.L.Trentelman@math.rug.nl., NL;(2) Department of Mathematics, University of Maastricht, P.O. Box 616, 6200 MD Maastricht, The Netherlands. P.Rapisarda@math.unimaas.nl., NL |
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Abstract: | In this paper new algorithms are developed for J-spectral factorization of polynomial matrices. These algorithms are based on the calculus of two-variable polynomial matrices and associated quadratic differential forms, and share the common feature that the problem is lifted from the original one-variable polynomial context to a two-variable polynomial context. The problem of polynomial J-spectral factorization is thus reduced to a problem of factoring a constant matrix obtained from the coefficient matrices of the polynomial matrix to be factored. In the second part of the paper, we specifically address the problem of computing polynomial J-spectral factors in the context of H ∞ control. For this, we propose an algorithm that uses the notion of a Pick matrix associated with a given two-variable polynomial matrix. Date received: January 1, 1998. Date revised: October 15, 1998. |
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Keywords: | . Polynomial J-spectral factorization Two-variable polynomial matrix Quadratic differential form Dissipativity Pick matrix. |
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