The Method of Lyapunov Function and Exponential Stability of Impulsive Delay Systems with Delayed Impulses

This paper investigates the exponential stability of general impulsive delay systems with delayed impulses. By using the Lyapunov function method, some Lyapunov-based sufficient conditions for exponential stability are derived, which are more convenient to be applied than those Razumikhin-type conditions in the literature. Their applications to linear impulsive systems with time-varying delays are also proposed, and a set of sufficient conditions for exponential stability is provided in terms of matrix inequalities. Meanwhile, two examples are discussed to illustrate the effectiveness and advantages of the results obtained.