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Minimal symmetric Darlington synthesis
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
2007 (English)In: MCSS. Mathematics of Control, Signals and Systems, ISSN 0932-4194, E-ISSN 1435-568X, Vol. 19, no 4, 283-311 p.Article in journal (Refereed) Published
Abstract [en]

We consider the symmetric Darlington synthesis of a p x p rational symmetric Schur function S with the constraint that the extension is of size 2p x 2p. Under the assumption that S is strictly contractive in at least one point of the imaginary axis, we determine the minimal McMillan degree of the extension. In particular, we show that it is generically given by the number of zeros of odd multiplicity of I (p)-SS*. A constructive characterization of all such extensions is provided in terms of a symmetric realization of S and of the outer spectral factor of I-p-SS*. The authors's motivation for the problem stems from Surface Acoustic Wave filters where physical constraints on the electro-acoustic scattering matrix naturally raise this mathematical issue.

Place, publisher, year, edition, pages
2007. Vol. 19, no 4, 283-311 p.
Keyword [en]
symmetric Darlington synthesis, inner extension, McMillan degree, Riccati equation, symmetric Potapov factorization, systems, matrix
URN: urn:nbn:se:kth:diva-17094DOI: 10.1007/s00498-007-0020-xISI: 000250632200001ScopusID: 2-s2.0-35948964080OAI: diva2:335137
QC 20100525Available from: 2010-08-05 Created: 2010-08-05 Last updated: 2012-02-23Bibliographically approved

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Enqvist, Per
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