A hierarchy of LMI inner approximations of the set of stable polynomials
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F11%3A00180622" target="_blank" >RIV/68407700:21230/11:00180622 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.automatica.2011.02.026" target="_blank" >http://dx.doi.org/10.1016/j.automatica.2011.02.026</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.automatica.2011.02.026" target="_blank" >10.1016/j.automatica.2011.02.026</a>
Alternative languages
Result language
angličtina
Original language name
A hierarchy of LMI inner approximations of the set of stable polynomials
Original language 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 thehierarchy 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.
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BC - Theory and management systems
OECD FORD branch
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Result continuities
Project
<a href="/en/project/GAP103%2F10%2F0628" target="_blank" >GAP103/10/0628: Semidefinite programming for nonlinear dynamical systems</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2011
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Automatica
ISSN
0005-1098
e-ISSN
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Volume of the periodical
47
Issue of the periodical within the volume
4
Country of publishing house
GB - UNITED KINGDOM
Number of pages
6
Pages from-to
1455-1460
UT code for WoS article
000292074400019
EID of the result in the Scopus database
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