TY - GEN
T1 - Stability Analysis of a Nonlinear System with Infinite Distributed Delays Describing Cell Dynamics
AU - Djema, W.
AU - Mazenc, F.
AU - Bonnet, C.
AU - Clairambault, J.
AU - Fridman, E.
N1 - Publisher Copyright: © 2018 AACC.
PY - 2018/8/9
Y1 - 2018/8/9
N2 - 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.
AB - 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.
KW - Exponential Stability
KW - Infinite Distributed Delay
KW - Lyapunov-Krasovskii Functionals (LKFs)
UR - http://www.scopus.com/inward/record.url?scp=85052566219&partnerID=8YFLogxK
U2 - 10.23919/ACC.2018.8430869
DO - 10.23919/ACC.2018.8430869
M3 - منشور من مؤتمر
SN - 9781538654286
T3 - Proceedings of the American Control Conference
SP - 1220
EP - 1223
BT - 2018 Annual American Control Conference, ACC 2018
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2018 Annual American Control Conference, ACC 2018
Y2 - 27 June 2018 through 29 June 2018
ER -