About: A hierarchy of LMI inner approximations of the set of stable polynomials

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
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. (en)
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 (en)
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 (en)
skos:notation	RIV/68407700:21230/11:00180622!RIV12-GA0-21230___
http://linked.open...avai/predkladatel	Fakulta elektrotechnická
http://linked.open...avai/riv/aktivita	P
http://linked.open...avai/riv/aktivity	P(GAP103/10/0628)
http://linked.open...iv/cisloPeriodika	4
http://linked.open...vai/riv/dodaniDat	2012
http://linked.open...aciTvurceVysledku	Henrion, Didier
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	České vysoké učení technické v Praze / Fakulta elektrotechnická
http://linked.open...dnocenehoVysledku	183839
http://linked.open...ai/riv/idVysledku	RIV/68407700:21230/11:00180622
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Stability; Positive polynomials; LMI; Toeplitz matrices (en)
http://linked.open.../riv/klicoveSlovo	LMI Positive polynomials Stability Toeplitz matrices
http://linked.open...odStatuVydavatele	GB - Spojené království Velké Británie a Severního Irska
http://linked.open...ontrolniKodProRIV	[54CF01E9CEF6]
http://linked.open...i/riv/nazevZdroje	Automatica
http://linked.open...in/vavai/riv/obor	BC
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	2 (xsd:int)
http://linked.open...vavai/riv/projekt	Semidefinite programming for nonlinear dynamical systems
http://linked.open...UplatneniVysledku	2011
http://linked.open...v/svazekPeriodika	47
http://linked.open...iv/tvurceVysledku	Ait Rami, M. Henrion, Didier
http://linked.open...ain/vavai/riv/wos	000292074400019
issn	0005-1098
number of pages	6 (xsd:int)
http://bibframe.org/vocab/doi	10.1016/j.automatica.2011.02.026
http://localhost/t...ganizacniJednotka	21230
is http://linked.open...avai/riv/vysledek of	A hierarchy of LMI inner approximations of the set of stable polynomials A hierarchy of LMI inner approximations of the set of stable polynomials

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