06047708

j

06047708 Wu, Shu-Lin Li, Ke-Lin Zhang, Jin-Shan Exponential stability of discrete-time neural networks with delay and impulses. Appl. Math. Comput. 218, No. 12, 6972-6986 (2012). 2012 Elsevier Science Publishing Co. (North-Holland), New York EN discrete-time neural networks variable delay impulses exponential stability discretization methods

doi:10.1016/j.amc.2011.12.079

Summary: 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 [{\it W.H. Chen}, {\it 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 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 different discretization methods.