Uniform stability with respect to the impulsive perturbations of the solutions of impulsive differential equations

Abstract

The notions of strong uniform stability of the zero solution of systems of differential equations and uniform stability with respect to the impulsive perturbations of the zero solution of systems of impulsive differential equations are introduced. The main results are given in two theorems. The first contains sufficient conditions under which the strong uniform stability of the zero solution of the respective system without impulses implies uniform stability with respect to the impulsive perturbations of the zero solution of the initial system with impulses. In the second theorem sufficient conditions are given under which the uniform Lipschitz stability of the zero solution of the respective system without impulses implies uniform stability with respect to the impulsive perturbations of the zero solution of the initial system with impulses.