Global exponential stability of static neural networks with delay and impulses: Discrete-time case

In this paper, we investigate the exponential stability of discrete-time static neural networks with impulses and variable time delay. The discrete-time neural networks are derived by discretizing the corresponding continuous-time counterparts with implicit-explicit-θ (IMEX-θ) method. The impulses are classified into three classes: input disturbances, stabilizing and “neutral” type— the impulses are neither helpful for stabilizing nor destabilizing the neural networks, and then by using a very excellent ideology introduced recently the connections between the impulses and the utilized Lyapunov function are fully explored with respect to each type of impulse. New analysis techniques that used to realize the ideology in discrete-time situation are proposed and it is shown that they are essentially different from the ones used in continuous-time case. Several criteria for global exponential stability of the static neural networks in discrete-time case are established in terms of linear matrix inequalities (LMIs) and numerical simulations are given to validate the obtained theoretical results.