Skip Navigation



IMA Journal of Mathematical Control and Information Advance Access published online on February 23, 2007
IMA Journal of Mathematical Control and Information, doi:10.1093/imamci/dnm007
This Article
Right arrow Full Text (PDF)
Right arrow All Versions of this Article:
24/4/523    most recent
dnm007v1
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Melchor-Aguilar, D.
Right arrow Articles by Niculescu, S.-I.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© 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 20 May 2006; Accepted on 8 January 2007


  Abstract

In this paper, we propose various estimates of the attraction region for a class of nonlinear time-delay systems of the form Formula(t) = Ax(t) + Bx(t – h(t)) + f(x(t), x(t – h(t))). 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.


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer:
Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.