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Block discrete-time schwarz form of multivariable rational interpolant and positivity by linear matrix inequality
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
2009 (English)In: European Signal Processing Conference, 2009, 393-397 p.Conference paper, Published paper (Refereed)
Abstract [en]

The state-space realization of a multivariable rational interpolant with bounded McMillan degree is given by the block discrete-time Schwarz form. A characterization of the positive realness of the block discrete-time Schwarz form is given by a linear matrix inequality.

Place, publisher, year, edition, pages
2009. 393-397 p.
Keyword [en]
Block discrete-time Schwarz form, multivariable interpolation, linear matrix inequality
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-14228Scopus ID: 2-s2.0-84863753439OAI: oai:DiVA.org:kth-14228DiVA: diva2:331820
Conference
17th European Signal Processing Conference, EUSIPCO 2009; Glasgow; United Kingdom; 24 August 2009 through 28 August 2009
Note

QC 20140923. Updated from manuscript to conference paper

Available from: 2010-07-27 Created: 2010-07-27 Last updated: 2014-09-23Bibliographically 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.
Series
Trita-MAT. OS, ISSN 1401-2294 ; 09:04
National Category
Mathematics Computational Mathematics
Identifiers
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)
Opponent
Supervisors
Note
QC 20100727Available from: 2009-06-03 Created: 2009-06-02 Last updated: 2010-07-27Bibliographically approved

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CiteExportLink to record
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Citation style
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Output format
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