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∈N. New sufficient conditions for exponential stability are derived using the method of Lyapunov functions. Illustrative examples are given as well.