Estimates for solutions of one class of systems of equations of neutral type with distributed delay

In the paper we consider a system of linear differential equations of neutral type with periodic coefficients and with distributed delay. Sufficient conditions for the exponential stability of the zero solution of this system are given, estimates for solutions that characterize the exponential decrease at infinity are indicated. In the study of exponential stability, the modified Lyapunov–Krasovskii functional is used. Also for system of delay difference equations, a criterion for the exponential stability of the zero solution in terms of the solvability of the matrix equation with a delayed argument is proved.