Exponential stability of solutions to nonlinear time-delay systems of neutral type

We consider a nonlinear time-delay system of neutral equations with constant coefficients in the linear terms $$ \frac{d}{dt}\big(y(t) + D y(t-\tau)\big) = A y(t) + B y(t-\tau) + F(t, y(t), y(t-\tau)), $$ where $$ \|F(t,u,v)\| \le q_1\|u\|^{1+\omega_1} + q_2\|v\|^{1+\omega_2}, \quad q_1, q_2, \omega_1, \omega_2 > 0. $$ We obtain estimates characterizing the exponential decay of solutions at infinity and estimates for attraction sets of the zero solution