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IMA Journal of Mathematical Control and Information Advance Access originally published online on February 23, 2007
IMA Journal of Mathematical Control and Information 2007 24(4):523-550; doi:10.1093/imamci/dnm007
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© The author 2007. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Estimates of the attraction region for a class of nonlinear time-delay systems

Daniel Melchor-Aguilar{dagger}

División of Matématics Aplicadas y Sistemas Computacionales, Instituto Potosino de Investigación Científica y Technológica, A.P.3-74, 78216 San Luis Potosí, SLP, México

Silviu-Iulian Niculescu{ddagger}

Laboratoire des Signaux et Systèmes (L2S, UMR CNRS 8506), Centre National de la Recherche Scientifique-Supélec, 3 rue Joliot Curie, 91190 Gif-sur-Yvette, France

{dagger} Email: dmelchor{at}ipicyt.edu.mx

{ddagger} Email: silviu.niculescu{at}lss.supelec.fr

Received on May 20, 2006; Accepted on January 8, 2007

In this paper, we propose various estimates of the attraction region for a class of nonlinear time-delay systems of the form Formula The approach is constructive and makes use of a Lyapunov–Krasovskii functional associated to the linear part. Several illustrative examples (delayed logistic equation, stabilizing nonlinear oscillations by delayed output feedback, congestion control in high-performance networks and hereditary phenomena in physics) complete the presentation.

Keywords: nonlinear time-delay systems; attraction region; Lyapunov–Krasovskii functionals.


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