@article{26335a6536a94ef4907cd65bbc0c23eb,
title = "Analysis of polynomial systems with time delays via the sum of squares decomposition",
abstract = "We present a methodology for analyzing robust independent-of-delay and delay-dependent stability of equilibria of systems described by nonlinear Delay Differential Equations by algorithmically constructing appropriate Lyapunov-Krasovskii functionals using the sum of squares decomposition of multivariate polynomials and semidefinite programming. We illustrate the methodology using an example from population dynamics.",
keywords = "Linear matrix inequality (LMI), Lyapunov-Krasovskii, Sum of squares (SOS), Time delay",
author = "Antonis Papachristodoulou and Peet, {Mathew M.} and Sanjay Lall",
note = "Funding Information: Manuscript received July 31, 2007; revised March 14, 2008. Current version published May 13, 2009. This work was supported in part by the Engineering and Physical Sciences Research Council Grant EP/E05708X/1. Recommended by Guest Editors G. Chesi and D. Henrion. A. Papachristodoulou is with the Department of Engineering Science, University of Oxford, Oxford OX1 3PJ, U.K. (e-mail: antonis@eng.ox.ac.uk). M. M. Peet is with the Department of Mechanical, Materials, and Aerospace Engineering, Illinois Institute of Technology, Chicago, IL 60616 USA (e-mail: mpeet@iit.edu). S. Lall is with the Department of Aeronautics and Astronautics, Stanford University, Stanford, CA 94305 USA (e-mail: lall@stanford.edu). Digital Object Identifier 10.1109/TAC.2009.2017168",
year = "2009",
doi = "10.1109/TAC.2009.2017168",
language = "English (US)",
volume = "54",
pages = "1058--1064",
journal = "IEEE Transactions on Automatic Control",
issn = "0018-9286",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
number = "5",
}