一类固定时刻脉冲微分系统的Φ-变差稳定性

Φ-variational Stability for a Class of Impulsive Differential Systems at Fixed Times

本文借助Φ-有界变差函数理论,以及一类不连续系统的Φ-有界变差解的稳定性理论,讨论了一类固定时刻脉冲微分系统的Φ-变差稳定性,给出了该类脉冲微分系统的Φ-变差稳定、Φ-变差吸引以及渐近Φ-变差稳定的定义,建立了该类脉冲微分系统Φ-有界变差解的Φ-变差稳定性和渐近Φ-变差稳定性的Lyapunov型定理.

By applying the theories of the bounded Φ-variation function and the Φ-variational stability for a class of discontinuous systems,the stability for a class of impulsive differential systems at fixed times is discussed in this paper.With respect to this kind of impulsive differential systems,the Φ-variational stability,attraction and asymptotically stability are defined.Finally,the Lyapunov type theorems of Φ-variational stability and asymptotically Φ-variational stability for one order impulsive differential systems are established.