References$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_upper_j_idt152",{id:"formSmash:upper:j_idt152",widgetVar:"widget_formSmash_upper_j_idt152",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:upper:referencesLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_upper_j_idt153_j_idt156",{id:"formSmash:upper:j_idt153:j_idt156",widgetVar:"widget_formSmash_upper_j_idt153_j_idt156",target:"formSmash:upper:j_idt153:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});

A Parameterization of Positive Real Residue Interpolants with McMillan Degree ConstraintPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2009 (English)Doctoral thesis, comprehensive summary (Other academic)
##### Abstract [en]

##### 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: 978-91-7415-343-9OAI: oai:DiVA.org:kth-10607DiVA: diva2:220740
##### Public defence

2009-06-12, Sal D1, Lindstedtsvägen 17, KTH, Stockholm, 10:00 (English)
##### Opponent

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##### Supervisors

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#####

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##### Note

QC 20100727Available from: 2009-06-03 Created: 2009-06-02 Last updated: 2010-07-27Bibliographically approved
##### List of papers

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.

1. A Parameterization of Positive Real Residue Interpolants with McMillan Degree Constraint$(function(){PrimeFaces.cw("OverlayPanel","overlay331819",{id:"formSmash:j_idt503:0:j_idt507",widgetVar:"overlay331819",target:"formSmash:j_idt503:0:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

2. Block discrete-time schwarz form of multivariable rational interpolant and positivity by linear matrix inequality$(function(){PrimeFaces.cw("OverlayPanel","overlay331820",{id:"formSmash:j_idt503:1:j_idt507",widgetVar:"overlay331820",target:"formSmash:j_idt503:1:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

3. A Robust Controller Synthesis for Mismatch of Delay by Nevanlinna-Pick Interpolation$(function(){PrimeFaces.cw("OverlayPanel","overlay331821",{id:"formSmash:j_idt503:2:j_idt507",widgetVar:"overlay331821",target:"formSmash:j_idt503:2:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

4. A Smith Predictor Synthesis for Unstable Plant by Nevanlinna-Pick Interpolation$(function(){PrimeFaces.cw("OverlayPanel","overlay331833",{id:"formSmash:j_idt503:3:j_idt507",widgetVar:"overlay331833",target:"formSmash:j_idt503:3:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

5. A Generalized Kullback-Leibler Approximation of Spectral Density with Tangential Second-order Statistics$(function(){PrimeFaces.cw("OverlayPanel","overlay331828",{id:"formSmash:j_idt503:4:j_idt507",widgetVar:"overlay331828",target:"formSmash:j_idt503:4:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

6. A Note on Schur Polynomial and Toeplitz Matrix$(function(){PrimeFaces.cw("OverlayPanel","overlay331834",{id:"formSmash:j_idt503:5:j_idt507",widgetVar:"overlay331834",target:"formSmash:j_idt503:5:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

References$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_lower_j_idt1196",{id:"formSmash:lower:j_idt1196",widgetVar:"widget_formSmash_lower_j_idt1196",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:lower:referencesLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_lower_j_idt1197_j_idt1199",{id:"formSmash:lower:j_idt1197:j_idt1199",widgetVar:"widget_formSmash_lower_j_idt1197_j_idt1199",target:"formSmash:lower:j_idt1197:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});