Asymptotical stability for a class of discrete systems with variable delay

In this paper, based on the discrete Wirtinger inequality, the problem of summation inequality is investigated. Some new summation inequalities are established, which extend the discrete Jensen inequality effectively. As an application of the summation inequalities, a novel sufficient criterion on asymptotical stability of discrete systems with variable delay is proposed. A numerical example is provided to show that our stability criterion achieves the improvements over the existing ones.