SOS for nonlinear delayed models in biology and networking

Antonis Papachristodoulou, Matthew M. Peet

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In this chapter we illustrate how the Sum of Squares decomposition can be used for understanding the stability properties of models of models of biological and communication networks. The models we consider are in the form of nonlinear delay differential equations with multiple, incommensurate delays. Using the sum of squares approach, appropriate Lyapunov-Krasovskii functionals can be constructed, both for testing delay-independent and delay-dependent stability. We illustrate the methodology using examples from congestion control for the Internet and gene regulatory networks.

Original languageEnglish (US)
Title of host publicationTopics in Time Delay Systems
Subtitle of host publicationAnalysis, Algorithms and Contr
EditorsJean Jacques Loiseau, Wim Michiels, Silviu-Iulian Niculescu, Rifat Sipahi
Pages133-143
Number of pages11
DOIs
StatePublished - Oct 19 2009
Externally publishedYes

Publication series

NameLecture Notes in Control and Information Sciences
Volume388
ISSN (Print)0170-8643

ASJC Scopus subject areas

  • Library and Information Sciences

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  • Cite this

    Papachristodoulou, A., & Peet, M. M. (2009). SOS for nonlinear delayed models in biology and networking. In J. J. Loiseau, W. Michiels, S-I. Niculescu, & R. Sipahi (Eds.), Topics in Time Delay Systems: Analysis, Algorithms and Contr (pp. 133-143). (Lecture Notes in Control and Information Sciences; Vol. 388). https://doi.org/10.1007/978-3-642-02897-7_12