Razumikhin-type theorems for time-delay systems with Persistent impulses

The main results of the paper are generalizations of the Razumikhin classical theorems for stability analysis of impulsive time-delay systems. By employing Lyapunov-Razumikhin method and impulsive control theory, several Razumikhin-type theorems for uniform stability and global exponential stability are obtained. The significance and novelty of the results lie in that the criteria for stability of impulsive time-delay systems admit the existence of persistent impulses and unbounded time-varying delays. Two examples are provided to show the effectiveness of the proposed results.