Semidefinite approximations of the polynomial abscissa

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F16%3A00243325" target="_blank" >RIV/68407700:21230/16:00243325 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1137/15M1033198" target="_blank" >http://dx.doi.org/10.1137/15M1033198</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1137/15M1033198" target="_blank" >10.1137/15M1033198</a>

Result language
angličtina
Original language name
Semidefinite approximations of the polynomial abscissa
Original language description
Given a univariate polynomial, its abscissa is the maximum real part of its roots. The abscissa arises naturally when controlling linear differential equations. As a function of the polynomial coefficients, the abscissa is Hölder continuous, and not locally Lipschitz in general, which is a source of numerical difficulties for designing and optimizing control laws. In this paper we propose simple approximations of the abscissa given by polynomials of fixed degree, and hence controlled complexity. Our approximations are computed by a hierarchy of finite-dimensional convex semidefinite programming problems. When their degree tends to infinity, the polynomial approximations converge in $L^1$ norm to the abscissa, either from above or from below.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
<a href="/en/project/GA16-19526S" target="_blank" >GA16-19526S: Semidefinite programming certification of control laws for emerging transportation projects</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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