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Statements

Subject Item
n2:RIV%2F68407700%3A21230%2F11%3A00180622%21RIV12-GA0-21230___
rdf:type
skos:Concept n12:Vysledek
dcterms:description
Exploiting spectral properties of symmetric banded Toeplitz matrices, we describe simple sufficient conditions for the positivity of a trigonometric polynomial formulated as linear matrix inequalities (LMIs) in the coefficients. As an application of these results, we derive a hierarchy of convex LMI inner approximations (affine sections of the cone of positive definite matrices of sizem) of the nonconvex set of Schur stable polynomials of given degree n < m. It is shown that when m tends to infinity the hierarchy converges to a lifted LMI approximation (projection of an LMI set defined in a lifted space of dimension quadratic in n) already studied in the technical literature. An application to robust controller design is described. Exploiting spectral properties of symmetric banded Toeplitz matrices, we describe simple sufficient conditions for the positivity of a trigonometric polynomial formulated as linear matrix inequalities (LMIs) in the coefficients. As an application of these results, we derive a hierarchy of convex LMI inner approximations (affine sections of the cone of positive definite matrices of sizem) of the nonconvex set of Schur stable polynomials of given degree n < m. It is shown that when m tends to infinity the hierarchy converges to a lifted LMI approximation (projection of an LMI set defined in a lifted space of dimension quadratic in n) already studied in the technical literature. An application to robust controller design is described.
dcterms:title
A hierarchy of LMI inner approximations of the set of stable polynomials A hierarchy of LMI inner approximations of the set of stable polynomials
skos:prefLabel
A hierarchy of LMI inner approximations of the set of stable polynomials A hierarchy of LMI inner approximations of the set of stable polynomials
skos:notation
RIV/68407700:21230/11:00180622!RIV12-GA0-21230___
n12:predkladatel
n13:orjk%3A21230
n4:aktivita
n15:P
n4:aktivity
P(GAP103/10/0628)
n4:cisloPeriodika
4
n4:dodaniDat
n5:2012
n4:domaciTvurceVysledku
Henrion, Didier
n4:druhVysledku
n17:J
n4:duvernostUdaju
n9:S
n4:entitaPredkladatele
n18:predkladatel
n4:idSjednocenehoVysledku
183839
n4:idVysledku
RIV/68407700:21230/11:00180622
n4:jazykVysledku
n19:eng
n4:klicovaSlova
Stability; Positive polynomials; LMI; Toeplitz matrices
n4:klicoveSlovo
n7:Stability n7:Toeplitz%20matrices n7:Positive%20polynomials n7:LMI
n4:kodStatuVydavatele
GB - Spojené království Velké Británie a Severního Irska
n4:kontrolniKodProRIV
[54CF01E9CEF6]
n4:nazevZdroje
Automatica
n4:obor
n11:BC
n4:pocetDomacichTvurcuVysledku
1
n4:pocetTvurcuVysledku
2
n4:projekt
n16:GAP103%2F10%2F0628
n4:rokUplatneniVysledku
n5:2011
n4:svazekPeriodika
47
n4:tvurceVysledku
Ait Rami, M. Henrion, Didier
n4:wos
000292074400019
s:issn
0005-1098
s:numberOfPages
6
n14:doi
10.1016/j.automatica.2011.02.026
n8:organizacniJednotka
21230