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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.
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: urn:nbn:se:kth:diva-10607ISBN: 978-91-7415-343-9 (print)OAI: oai:DiVA.org:kth-10607DiVA: diva2:220740
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
List of papers
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
(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
Positive real interpolation, McMillan degree constraint
National Category
Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-14227 (URN)
Note
QC20100727Available from: 2010-07-27 Created: 2010-07-27 Last updated: 2010-07-27Bibliographically approved
2. Block discrete-time schwarz form of multivariable rational interpolant and positivity by linear matrix inequality
Open this publication in new window or tab >>Block discrete-time schwarz form of multivariable rational interpolant and positivity by linear matrix inequality
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.

Keyword
Block discrete-time Schwarz form, multivariable interpolation, linear matrix inequality
National Category
Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-14228 (URN)2-s2.0-84863753439 (Scopus ID)
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
3. A Robust Controller Synthesis for Mismatch of Delay by Nevanlinna-Pick Interpolation
Open this publication in new window or tab >>A Robust Controller Synthesis for Mismatch of Delay by Nevanlinna-Pick Interpolation
(English)Manuscript (preprint) (Other academic)
Abstract [en]

In this paper, a robust controller synthesis for the mismatch of delay in terms of the Nevanlinna-Pick interpolation is presented.

Keyword
Mismatch of delay, robust stability, Nevanlinna-Pick interpolation
National Category
Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-14229 (URN)
Note
QC20100727Available from: 2010-07-27 Created: 2010-07-27 Last updated: 2010-07-27Bibliographically approved
4. A Smith Predictor Synthesis for Unstable Plant by Nevanlinna-Pick Interpolation
Open this publication in new window or tab >>A Smith Predictor Synthesis for Unstable Plant by Nevanlinna-Pick Interpolation
(English)Manuscript (preprint) (Other academic)
Keyword
Time delay system, modified Smith predictor, Nevalinna-Pick interpolation
National Category
Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-14235 (URN)
Note
QC20100727Available from: 2010-07-27 Created: 2010-07-27 Last updated: 2010-07-27Bibliographically approved
5. A Generalized Kullback-Leibler Approximation of Spectral Density with Tangential Second-order Statistics
Open this publication in new window or tab >>A Generalized Kullback-Leibler Approximation of Spectral Density with Tangential Second-order Statistics
(English)Manuscript (preprint) (Other academic)
Abstract [en]

In this paper, we study an approximation of spectral density in terms of the generalized Kullback-Leibler distance minimization. For a given spectral density, we seek a spectral density by minimizing the generalized Kullback-Leibler distance subject to a constraint on the tangential second-order statistics.

Keyword
Generalized Kullback-Leibler distance, tangential Nevanlinna-Pick interpolation
National Category
Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-14231 (URN)
Note
QC20100727Available from: 2010-07-27 Created: 2010-07-27 Last updated: 2010-07-27Bibliographically approved
6. A Note on Schur Polynomial and Toeplitz Matrix
Open this publication in new window or tab >>A Note on Schur Polynomial and Toeplitz Matrix
(English)Manuscript (preprint) (Other academic)
Keyword
Schur polynomial, Toeplitx matrix, annihilator
National Category
Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-14236 (URN)
Note
QC20100727Available from: 2010-07-27 Created: 2010-07-27 Last updated: 2010-07-27Bibliographically approved

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