Abstract
Lyapunov theorems did not tell us how to choose the Lyapunov function to analyze the stability of equilibrium states for nonlinear systems, and currently there is no particular way or formula that can guide us on how to choose the right Lyapunov function when using Lyapunov theorems and LaSalle theorems. Typically, a Lyapunov candidate function is chosen based on the trial and error approach. In this paper, the author presents an approach that is able to guide us to choose the right Lyapunov function based on the initial random Lyapunov candidate function when using LaSalle theorems to study the equilibrium states’ stability for the nonlinear systems. Difference case studies are given in the paper in order to show the effectiveness of the approach.
