Routh-Hurwitz Conditions and Lyapunov Second Method for a Nonlinear System

In this paper, a Lyapunov function is generated to determine the domain of asymptotic stability of a system of three first order nonlinear ordinary differential equations describing the behaviour of a nuclear spin generator (NSG). The generated Lyapunov function, is a simple quadratic form, whose coefficients are chosen so that the Routh-Hurwitz criteria are satisfied for the corresponding linear differential equations.