The study of dynamic systems with impulsive effects has attracted the attention of many scientific investigators because of its importance in the applied sciences. It is well known that stability is fundamental in the analysis and design of control systems. In many systems under consideration, the origin is not necessarily an equilibrium point, and it is desired to bring a set of states close to a certain state. This has led to the introduction of the notion of practical stability. The authors have provided conditions that are sufficient for the uniform exponential stability of perturbed impulsive systems using the second method of Lyapunov.
The paper is well written and of normal length; I can point out few drawbacks. All functions are bounded, since they are continuous, defined on the ball centered at the origin, and of radius r. In Definition 4.1, the authors do not explain the relation between ϱ and r. A simple comparison between assumptions (A3) and (A5) shows that &mgr;k = &egr; {k}r2. Hence, (A5) might not be needed. The paper is not well documented; readers will need to consult other resources for more detailed background information.
