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A Note on Schur Polynomial and Toeplitz Matrix
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
(English)Manuscript (preprint) (Other academic)
Keyword [en]
Schur polynomial, Toeplitx matrix, annihilator
National Category
Computational Mathematics
URN: urn:nbn:se:kth:diva-14236OAI: diva2:331834
QC20100727Available from: 2010-07-27 Created: 2010-07-27 Last updated: 2010-07-27Bibliographically approved
In thesis
1. A Parameterization of Positive Real Residue Interpolants with McMillan Degree Constraint
Open this publication in new window or tab >>A Parameterization of Positive Real Residue Interpolants with McMillan Degree Constraint
2009 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The main body of this thesis consists of six appended papers.The papers are about the theory of the positive real interpolationwith McMillan degree constraint.In Paper A, a parameterization of the positive real residue interpolantswith McMillan degree constraint is given.For a given interpolation data and for each free parameter,a positive real interpolant, of which McMillan degree isequal to the McMillan degree of the maximum entropy interpolant, is obtained bysolving a nonlinear equation, which is homotopic to a nonlinear equation to determinethe maximum entropy interpolant.In Paper B,the state-space realization of the multivariable rational interpolant with bounded McMillan degreeis given by the block discrete-time Schwarz form.A characterization of the positive realness of the block discrete-time Schwarz form isgiven by a linear matrix inequality.In Paper C,a robust controller synthesis for the mismatch of delay in terms ofthe Nevanlinna-Pick interpolation is presented.In Paper D,a Smith predictor synthesis for unstable and minimum-phaseinput delay system and for a first orderunstable distributed delay system is given in terms of the Nevanlinna-Pick interpolation.In Paper E , we study an approximation of spectral density in termsof the generalized Kullback-Leibler distance minimization.For a given spectral density,we seek a spectraldensity by minimizingthe generalized Kullback-Leibler distance subject to a constraint onthe tangential second-orderstatistics.In Paper F, a property of Schur polynomial of real coefficientsand real Toeplitz matrix is given.Suppose that the vector of coefficients of a Schur polynomial annihilatesa Toeplitz matrix, then the Toeplitz matrix is in facta zero matrix.

Place, publisher, year, edition, pages
Stockholm: KTH, 2009. viii, 13 p.
Trita-MAT. OS, ISSN 1401-2294 ; 09:04
National Category
Mathematics Computational Mathematics
urn:nbn:se:kth:diva-10607 (URN)978-91-7415-343-9 (ISBN)
Public defence
2009-06-12, Sal D1, Lindstedtsvägen 17, KTH, Stockholm, 10:00 (English)
QC 20100727Available from: 2009-06-03 Created: 2009-06-02 Last updated: 2010-07-27Bibliographically approved

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Kuroiwa, Yohei
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