Exponential stability of linear discrete systems with constant coefficients and single delay

In the paper the exponential stability and exponential estimation of the norm of solutions to a linear system of difference equations with single delay x (k + 1) = Ax (k) + Bx (k − m) , k = 0, 1, . . . is studied, where A, B are square constant matrices and m \in N. New sufficient conditions for exponential stability are derived using the method of Lyapunov
functions. Illustrative examples are given as well.