Asymptotic stability in perturbed delay difference systems

Consider the delay difference system x(i)(n + 1) - x(i)(n) = -b(i)x(i)(n-l(i)(n)) + (m)Sigma(j=1)d(ij)(n)x(j)(n-h(ij)(n)), i, j = 1,2,...,m, where 0 less than or equal to li (n) less than or equal to li, 0 less than or equal to h(ij) (n) less than or equal to h(ij), \d(ij) (n)\ < d(ij), l(i), h(ij) are nonnegative integers, b(i) > 0, d(ij) greater than or equal to 0 are real constants. It is shown that the trivial solution of the above system is asymptotically stable if b(i)(l(i) + 1) < 3/2 + 1/2(li+1), i = 1,2...,m, and a certain matrix derived from the coefficient matrix is a nonsingular M-matrix. (C) 2004 Elsevier Inc. All rights reserved.