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

Walid Djema (1) , Frédéric Mazenc (2, 3) , Catherine Bonnet (2, 3) , Jean Clairambault (4) , Emilia Fridman (5)

1 BIOCORE - Biological control of artificial ecosystems
2 L2S - Laboratoire des signaux et systèmes
3 DISCO - Dynamical Interconnected Systems in COmplex Environments
4 MAMBA - Modelling and Analysis for Medical and Biological Applications
5 Department of Electrical Engineering and Systems at the School of Electrical Engineering

We want to reconcile some earlier mod-eling 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.

Mots clés: Exponential Stability; Infinite Distributed Delay; Lyapunov- Krasovskii Functionals (LKFs)

Domaines: Automatique

Walid Djema, Frédéric Mazenc, Catherine Bonnet, Jean Clairambault, Emilia Fridman. Stability Analysis of a Nonlinear System with Infinite Distributed Delays Describing Cell Dynamics. ACC 2018 - American Control Conference, Jun 2018, Milwaukee, United States. ⟨10.23919/acc.2018.8430869⟩. ⟨hal-01849010⟩