On the stability of solutions of a class of nonlinear nonautonomous systems with delay

A nonlinear time-delay system with nonlinearities of a sector type and nonstationary perturbations is studied. It is assumed that the zero solution of the corresponding unperturbed delay-free system is asymptotically stable. With the aid of the Razumikhin theorem, conditions are obtained under which the perturbations do not destroy the asymptotic stability for an arbitrary continuous nonnegative and bounded delay.