# Linear Equations with Stationary Coefficients

Chapter

## Abstract

Here the procedure of Lyapunov functionals construction described in Chap. 1 is applied to the difference equation with stationary coefficients in a general form. Four different ways of Lyapunov functionals construction are shown that allows to get four different types of sufficient conditions for asymptotic mean square stability of the trivial solution of the considered equation. One generalization of obtained stability conditions are shown also. Besides the special investigation of asymptotic behavior of the solution of difference equation via characteristic equation are shown. The results of investigations are illustrated by figures with obtained stability regions and trajectories of solutions.

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