Exponential stability of static neural networks with time delay and impulses

In this study, the authors investigate the problem of global exponential stability of static neural networks with time delay and impulses. Three types of impulses are studied: the impulses are input disturbances; the impulses are `neutral` type, that is, they are neither helpful for stability of neural networks nor destabilising; and the impulses are stabilising. For each type of impulses, by using Lyapunov function and Razumikhin-type techniques, sufficient conditions for global exponential stability are established in terms of linear matrix inequalities with respect to suitable classes of impulse time sequences. The new sufficient conditions can explicitly reveal the effects of time delay, impulses etc., on the stability. Numerical results are given to show the less conservatism of the obtained criteria compared with the existing ones.