Stability of Linear Discrete Systems with Variable Delays

The paper studies the stability of linear systems of difference equations with single delay x(k + 1) = Ax (k) + Sigma(l)(s=1) B-s(k)x(k - m(s)(k)), k = 0,1... where l >= 1, A is a constant n x n matrix, B-x(k) are n x n matrices. m(s)(k) is an element of N boolean OR {0} and In m(s) <= m for an m is an element of N. Sufficient conditions for the stability are derived using the method of Lyapunov functions.