STABILITY AND EXPONENTIAL STABILITY OF LINEAR DISCRETE SYSTEMS WITH CONSTANT COEFFICIENTS AND SINGLE DELAY

The paper investigates the exponential stability and exponential estimate of the norms of solutions to a linear system of difference equations with single delay
\begin{equation*}
x\left( {k+1} \right)=Ax\left( k \right)+Bx\left( {k-m} \right),
\quad k=0,1,\dots
\end{equation*}
where $A$, $B$ are square constant matrices and $m\in\mathbb{N}$. Sufficient conditions for exponential stability
are derived using the method of Lyapunov functions and its efficiency is demonstrated by examples.