Exponential stability of discrete-time neural networks with delay and impulses

In this paper, we investigate the exponential stability of discrete‐time neural networks with impulses and time‐varying delay. The discrete‐time neural networks are derived by discretizing the corresponding continuous‐time counterparts with different discretization methods. 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 the excellent ideology introduced recently by Chen and Zheng [W.H. Chen, W.X. Zheng, Global exponential stability of impulsive neural networks with variable delay: an LMI approach, IEEE Trans. Circuits Syst. I 56 (6) (2009) 1248–1259], the connections between the impulses and the utilized Lyapunov function are fully explored with respect to each type of impulse. Novel techniques that used to realize the ideology in discrete‐time situation are proposed and it is shown that they are essentially different from the continuous‐time case. Several criteria for global exponential stability of the discrete‐time neural networks are established in terms of matrix inequalities and based on these theoretical results numerical simulations are given to compare the capability of different discretization methods.