On the vector Lyapunov Functions and Asymptotic Eventual Stability for nonlinear Impulsive Differential Equations via Comparison Principle

In this paper, the asymptotic eventual stability of nonlinear impulsive differential equations with fixed moments of impulse is examined using the vector Lyapunov functions, which is generalized by a class of piecewise continuous Lyapunov functions. The novelty in the use of the vector Lypunov functions lies in the fact that the "restrictions" encountered by the scalar Lyapunov function is safely handled especially for large scale dynamical systems, since the method involves splitting the Lyapunov functions into components so that each of the components can easily describe the behavior of the solution state. Together with comparison results, sufficient conditions for the asymptotic eventual stability are presented.