Asymptotic stability in perturbed delay difference systems ✩

Consider the delay difference system xi(n+ 1) −xi (n)=−bixi n− li(n) + m j=1 dij (n)xj n− hij (n) , i, j = 1, 2, . . .,m, where 0 li(n) li, 0 hij (n) hij , |dij (n)| dij , li, hij are nonnegative integers, bi > 0, dij 0 are real constants. It is shown that the trivial solution of the above system is asymptotically stable if bi (li + 1) < 32 + 1 2(li+1) , i = 1, 2, . . .,m, and a certain matrix derived from the coefficient matrix is a nonsingular M-matrix.  2004 Elsevier Inc. All rights reserved