Impulsive stabilization of functional differential equations by Lyapunov-Razumikhin functions

A uniform stability theorem and a uniform asymptotic stability theorem are formulated, which show that certain impulsive perturbations may make unstable systems uniformly stable, even uniformly asymptotically stable. The method is based on Lyapunov-like functions coupled with certain Razumikhin techniques. Difficulties created by the special features possessed by impulsive functional differential equations are overcome by using a more complicated analysis. Also, since the unperturbed systems may be unstable, the Traditional Lyapunov-Razumikhin methods in the treatment of functional differential equations were modified.