On stability of first order linear impulsive differential equations

In this paper, we focus on the stability problems of first order linear impulsive differential equations. We construct an ordinary differential equation representation of the impulsive system such that it is suitable for the qualitative analysis of the later. This process is achieved by a transformation that bijectively maps the solutions of the initial value problems for impulsive differential equations to the solutions of the initial value problems for ordinary differential equations. A relationship between stability properties of impulsive differential equations and the corresponding ordinary differential equations was established.