Estimates of the attraction region for a class of nonlinear time-delay systems

In this paper, we propose various estimates of the attraction region for a class of nonlinear time-delay systems of the form $\dot{x}(t)=Ax(t)+Bx(t-h(t))+f(x(t),x(t-h(h)))$ 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.