New robust stability condition for discrete-time recurrent neural networks with time-varying delays and nonlinear perturbations

In this paper, the robust delay-dependent stability problem is investigated for discrete-time recurrent neural networks (DRNNs) with time-varying delays and nonlinear perturbations. A novel summation inequality is proposed, which takes information on the double summation of system state into consideration and further extends the discrete Wirtinger-based inequality. By utilizing technique of the novel inequality and Lyapunov-Krasovskii functionals, a sufficient condition on robust stability of DRNNs with time-varying delays and nonlinear perturbations is obtained in terms of linear matrix inequality. The numerical example is included to show that the proposed method is effective and provides less conservative results.