Asymptotic Stability Condition for a Class of Linear Delay Difference Equations of Higher Order

AbstractIn this paper we obtain a necessary and sufficient condition for the asymptotic stability of the zero solution of the linear delay difference equationxn+1−xn+p∑j=1Nxn−k+(j−1)l=0,n=0,1,2,…,by using root-analysis for the characteristic equation. Here, p is a real number and k, l, and N are positive integers with k>(N−1)l