System stability analysis via a perturbation technique

In this paper, a discriminant for judging the stability of differential dynamical systems is given. The discriminant is a rational expression in the coefficients of the original system. How to transform a differential dynamical system to the normal form is shown, which is the origin of the discriminant. This method is more simple and practical than the traditional Lyapunov method. Examples are presented to show the applicability of the methodology and the convenience of the discriminant.