Stability of solutions of delay differential equations

In the present article, we consider a class of systems of linear differential equations with infinite distributed delay and periodic coefficients. We use the Lyapunov–Krasovskii functional and obtain sufficient conditions for exponential stability of the zero solution, find conditions on perturbation of the coefficients of the system that guarantee preservation of exponential stability, and establish estimates for the norms of solutions of the initial and perturbed systems that characterize exponential decay at infinity.