A Method to Find Stable Region of Nonlinear System

Abstract

This paper presents a new method of finding the region of asymptotic stability around the equilibrium point of a nonlinear system. It employs the idea of an inverse problem, that is, the problem to decide the system equation which is asymptotically stable inside a prescribed curve. Although the Liapunov. function is not used explicitly in this method, the fundamental thoughts originate in the stability theory of Liapunov. The presented method is so straightforward as to dispense with any groping which is often inevitable for finding Liapunov function. The example to find the region of asymptotic stability of van der Pol's system is presented to illustrate clearly how to apply the method to a particular given problem. The example has revealed that the method brings about extremely good accuracy in the comparatively small expense of calculation.