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A Parameterization of Positive Real Residue Interpolants with McMillan Degree Constraint
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
(English)Manuscript (preprint) (Other academic)
Abstract [en]

A parameterization of the solutions to the positive real residue interpolation with McMillan degree constraint is given. The McMillan degree of the interpolants is equal to the McMillan degree of the maximum entropy interpolant, and the parameterization includes the maximum entropy interpolant.

Keyword [en]
Positive real interpolation, McMillan degree constraint
National Category
Computational Mathematics
URN: urn:nbn:se:kth:diva-14227OAI: diva2:331819
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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