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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

  • Czech description

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

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

  • 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