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

In this paper we obtain a necessary and sufficient condition for the asymptotic stability of the zero solution of the linear delay difference equation N xnq1yxnqp xnykq jy1.ls0, ns0, 1, 2, . . . , js1 by using root-analysis for the characteristic equation. Here, p is a real number and k, l, and N are positive integers with k) Ny1.l.