Global exponential stability of delay difference equations with delayed impulses

This paper investigates the global exponential stability of delay difference equations with delayed impulses. By virtue of Lyapunov functions together with Razumikhin technique, a number of global exponential stability criteria are provided. Both the stability results that impulses act as perturbation and the stability results that impulses act as stabilizer are obtained. Some examples are also presented to illustrate the effectiveness of the obtained results. It should be noted that it is the first time that the Razumikhin type exponential stability results for delay difference equations with delayed impulses are given.