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In the paper, we consider systems of linear delay difference equations with periodic coefficients. We establish sufficient conditions for the asymptotic stability of the zero solution to the systems and obtain estimates of the stabilization rate of solutions at infinity. When obtaining the results we use a discrete analog of Lyapunov–Krasovskii functional.

In the present paper, we consider a class of functional difference equations with periodic coefficients. We establish criteria for asymptotic stability of the zero solution to the equations and obtain estimates characterizing the decay rates of solutions to these equations at infinity.