Estimates of the attraction region for a class of nonlinear time-delay systems
Résumé
In this paper, we propose various estimates of the attraction region for a class of nonlinear time-delay systems of the form ẋ=Ax(t) + (t - h (t) + f (x(t), x (t-h (t))) The approach is constructive and makes use of a Lyapunov-Krasovskii functional associated to the linear part. Several illustrative examples (delayed logistic equation, stabilizing nonlinear oscillations by delayed output feedback, congestion control in high-performance networks and hereditary phenomena in physics) complete the presentation. The author 2007. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications.