关键词: 广义Lyapunov函数, LaSalle不变原理, Zorn引理, 偏序, 非线性系统

Abstract:

Based on Zorn’s lemma and LaSalle’s invariance principle, the existence of the minimal generalized Lyapunov function for nonlinear systems was considered. We developed the minimal generalized Lyapunov function theorems and the minimal strong generalized Lyapunov function theorems for nonlinear dynamical systems.

Key words: generalized Lyapunov function, LaSalle’s invariance principle, Zorn’s lemma, partial order, nonlinear system