Exponential stability of impulsive discrete systems with time delay and applications in stochastic neural networks: A Razumikhin approach

Authors:
Sichao Wu;Chuandong Li;Xiaofeng Liao;Shukai Duan
Affiliations:
College of Computer, Chongqing University, Chongqing 400044, China;College of Computer, Chongqing University, Chongqing 400044, China;College of Computer, Chongqing University, Chongqing 400044, China;School of Electronics and Information Engineering, Southwest University, 400715 Chongqing, China
Venue:
Neurocomputing
Year:
2012

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Abstract

This paper investigates exponential stability of the equilibrium point of discrete-time delayed dynamic systems with impulsive effects. Firstly, some Razumikhin-type theorems considering stabilizing effects of impulses are introduced. These results show that even the impulse-free component of the original system is unstable; impulses may compensate the deviating trend. Then, we apply the theoretical results to a class of recurrent neural networks under stochastic perturbations and derive several stability preservation criteria; the applicable region of the impulsive strength is also estimated. Some numerical examples are provided to illustrate the efficiency of the results at the end.