A characterization of delay independent stability for linear off-diagonal delay difference equations

In this paper, we consider linear off-diagonal difference equations of the form (1)xi(k+1)=∑j=1naijxj(k−τij),fori=1,…,n,where A=(aij)1≤i,j≤n∈Rn×n and τ=(τij)1≤i,j≤n is the delay. Our main result is to establish an explicit characterization in terms of A for delay independent stability of (1). As an application, we establish a criterion for delay independent stability for an equilibrium of a discrete-time Lotka-Volterra equation.