New Results on Stability of Discrete-Time Impulsive Systems with Time Delays

This paper is concerned with the stability of discrete-time impulsive systems with time delays. Some new stability criteria are provided by employing Lyapunov functions together with Razumikhin technique. Sufficient conditions are established to guarantee that even if impulsive perturbations occur frequently in some time domains, stability of discrete-time impulsive delay systems can still be achieved if the impulsive intervals with low impulse frequency satisfy certain conditions, which makes the obtained criteria more practical in this paper. Moreover, application to a class of discrete-time impulsive neural networks is also considered. Finally, two numerical examples and a practical example are given to illustrate the effectiveness and superiority of the obtained results.