Delay dependent stability conditions of static recurrent neural networks: a non-linear convex combination method

A new method is developed for stability of static recurrent neural networks with time-varying delay in this study. Improved delay-dependent conditions in the form of a set of linear matrix inequalities are derived for this class of static nets through the newly proposed augmented Lyapunov-Krasovski functional. Our derivation employs a novel non-linear convex combination technique, that is, quadratic convex combination. Different from previous results, the property of quadratic convex function is fully taken advantage of without resort to the Jensen´s inequality. A numerical example is provided to verify the effectiveness and superiority of the presented results.