Razumikhin-type theorems on exponential stability of impulsive infinite delay differential systems

In this note, we study the exponential stability of impulsive functional differential systems with infinite delays by using the Razumikhin technique and Lyapunov functions. Several Razumikhin-type theorems on exponential stability are obtained, which shows that certain impulsive perturbations may make unstable systems exponentially stable. Some examples are discussed to illustrate our results.