Asymptotical stability of the exact solutions and the numerical solutions for a class of impulsive differential equations

This paper is concerned with stability and asymptotical stability of a class of impulsive delay differential equations (IDDEs). Stability and asymptotical stability of the system of IDDEs are studied by the properties of delay differential equations (DDEs) without impulsive perturbations. Base on this idea, numerical methods of IDDEs are constructed. Stability and asymptotical stability of numerical methods of IDDEs are also studied by the properties of numerical methods of DDEs.