Stability Analysis of a Nonlinear System with Infinite Distributed Delays Describing Cell Dynamics

W. Djema, F. Mazenc, C. Bonnet, J. Clairambault, E. Fridman

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

We want to reconcile some earlier modeling ways of the cell cycle in one common framework. Accordingly, we consider a model that contains a compartment where cells may be quiescent for an unlimited time, along with a proliferating phase in which most of the cells may divide, or die, while few of them may be arrested during their cycle for unlimited time. In fact, the cell-cycle arrest may occur for many reasons (DNA damages detected at some checkpoints, insufficient resources for cell grow, drug infusions). We actually extend some early models involving finite distributed delays (taken from [2], [1]) to the case of infinite distributed delays and time-varying parameters. Our main result relies on the construction of a novel Lyapunov-Krasovskii functional, suitable for the analysis of the origin of the system involving infinite distributed delays and time-varying parameters.

Original languageEnglish
Title of host publication2018 Annual American Control Conference, ACC 2018
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages1220-1223
Number of pages4
ISBN (Print)9781538654286
DOIs
StatePublished - 9 Aug 2018
Event2018 Annual American Control Conference, ACC 2018 - Milwauke, United States
Duration: 27 Jun 201829 Jun 2018

Publication series

NameProceedings of the American Control Conference
Volume2018-June
ISSN (Print)0743-1619

Conference

Conference2018 Annual American Control Conference, ACC 2018
Country/TerritoryUnited States
CityMilwauke
Period27/06/1829/06/18

Keywords

  • Exponential Stability
  • Infinite Distributed Delay
  • Lyapunov-Krasovskii Functionals (LKFs)

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