We consider the system x k+1=A kx k+b ku k,u= k+1=m k *x k,k=1,2,..., where A k ∈ ℝ n×n, b k ∈ ℝ n, and m k ∈ ℝ n. We assume that A k is a Frobenius matrix, the last component of vector b k is zero, and all entries of A k and b k are bounded for all k. Lyapunov quadratic function with diagonal matrix of coefficients is used to find coefficients m k and restrictions on coefficients b k which make the system globally asymptotically stable.