Stability and exponential stability of linear discrete systems with constant coefficients and single delay

This paper investigates the exponential stability and exponential estimate of the norms of solutions to a linear system of difference equations with single delay x(k+1)=Ax(k)+Bx(k−m),k=0,1,…where A, B are square constant matrices and m∈N. Sufficient conditions for exponential stability are derived using the method of Lyapunov functions and its efficiency is demonstrated by examples.