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

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.