一类不连续系统的Φ-变差稳定性

Φ-Variational Stability for a Class of Discontinuous Systems

本文借助Φ-有界变差函数理论,讨论了一类不连续系统的Φ-有界变差解的稳定性,给出了该类不连续系统的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Φ-有界变差解Φ-变差稳定性和渐近Φ-变差稳定性的Lyapunov型定理。该结果是对一类不连续系统变差稳定性定理的本质推广。

By using the bounded Φ-variation function,the stability of the bounded Φ-variation solu-tion to a class of discontinuous systems is discussed.With respect to this kind of discontinuous systems,the Φ-variational stability,the Φ-variational attraction and asymptotically Φ-variational stabklity are defined.The Lyapunov type theorems for the Φ-variational stability and asymptotically Φ-variational stability of the bounded Φ-variation solutions are established.This result is an essential generalization of the variational stability theorem for a class of discontinuous systems.