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Journal article
Contractive determinantal representations of stable polynomials on a matrix polyball
Mathematische Zeitschrift, v 283(1-2), pp 25-37
01 Jun 2016
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Abstract
We show that a polynomial p with no zeros on the closure of a matrix unit polyball, a.k.a. a cartesian product of Cartan domains of type I, and such that p(0) = 1, admits a strictly contractive determinantal representation, i.e., p = det(I - K Z(n)), where n = (n(1),...,n(k)) is a k-tuple of nonnegative integers, Z(n) = circle plus(k)(r= 1)(Z((r)) circle times I-nr), Z((r)) = [z(ij)((r))] are complex matrices, p is a polynomial in the matrix entries z(ij)((r)), and K is a strictly contractive matrix. This result is obtained via a noncommutative lifting and a theorem on the singularities of minimal noncommutative structured system realizations.
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Details
- Title
- Contractive determinantal representations of stable polynomials on a matrix polyball
- Creators
- Anatolii Grinshpan - Drexel UniversityDmitry S. Kaliuzhnyi-Verbovetskyi - Drexel UniversityVictor Vinnikov - Ben-Gurion University of the NegevHugo J. Woerdeman - Drexel University
- Publication Details
- Mathematische Zeitschrift, v 283(1-2), pp 25-37
- Publisher
- Springer Nature
- Number of pages
- 13
- Grant note
- DMS-0901628 / NSF; National Science Foundation (NSF) 2010432 / BSF Grant
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000374562900002
- Scopus ID
- 2-s2.0-84947791229
- Other Identifier
- 991019168407904721
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- Collaboration types
- Domestic collaboration
- International collaboration
- Web of Science research areas
- Mathematics