On the stability of systems of linear differential equations of neutral type with distributed delay

We consider one class of systems of nonautonomous linear differential equations of neutral type with distributed delay. We obtain sufficient conditions for the exponential stability of the zero solution and conditions on perturbations of the coefficients under which the exponential stability of the zero solution is preserved. Using a Lyapunov–Krasovskiĭ functional of a special kind, we prove some estimates that characterize the exponential decay of solutions at infinity.