On the null-controllability of nonlinear delay systems with restrained controls

Sufficient conditions are developed for the null-controllability of the nonlinear delay process (1) $\text{x}\text{?}\text{(t) = L(t, x}{}_{\mathrm{t}}\text{) + B(t) u(t) + f(t, x}{}_{\mathrm{t}}\text{, u(t))}$ when the values of the control functions u lie in an m-dimensional unit cube C^m of E^m. Conditions are placed on f which guarantee that if the uncontrolled system $\text{x}\text{?}\text{(t) = L(t, x}{}_{\mathrm{t}}\text{)}$ is uniformly asymptotically stable and if the linear control system x(t) = L(t, x_t) + B(t) u(t) is proper, then (1) is null-controllable.