On the ellipsoidal bounds of the reachable set for a class of time-delayed nonlinear systems with bounded input

We address the problem of finding an ellipsoid to bound the set of the states that are reachable from the origin in finite time for Lure-type systems with time-varying delays and bounded input. The time-varying delays appear both in the linear and nonlinear parts of the Lure system, whereby the bound on the delay's magnitude and rate is known. A Lyapunov-Krasovskii type functional is used to obtain a bounding ellipsoid by solving linear matrix inequalities which are delay dependent. We illustrate the applicability of our results on an example derived from models of neuronal populations.