Nonlinear Systems Stability Analysis

2.3 LYAPUNOV FUNCTION GENERATION FOR NONLINEAR AUTONOMOUS SYSTEMS [n1]³

This section is a survey of methods for generating Lyapunov functions. More specifically, an attempt has been made to bring together in one place, and relate to one another, some of the various techniques for generating Lyapunov functions. A review of the definitions and the theorems of stability in Section 2.2 is recommended for a better understanding of this section.

Before getting involved in generating Lyapunov functions for the following nonlinear systems:

$\dot{x}=f\left(x\right),$

(2.17)

it seems reasonable if we first try to linearize the nonlinear system of (2.17) about the equilibrium state. By expanding and evaluating the nonlinear vector function f(x) in the Taylor series expansion ...