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