A Criterion for the Stability of Motion of Nonlinear Systems

As to an autonomous nonlinear system, the stability of the equilibrium slate in a sufficiently small neighborhood of the equilibrium state can be determined by eigen values of the linear pan of the nonlinear system provided that the eigenvalues are not in a critical case.Many methods may be used to detect the stability for a linear system.A lot of researches for determining the stability of a nonlinear system are completed by mathematicians and mechanicians but most of them are methods for the special forms of nonlinear systems.Till now.none of these methods can be conveniently applied to all nonlinear systems.The method introduced by this paper gives the necessary and sufficient conditions of the stability of a nonlinear system.The familiar Krasoyski's method is a special case of this method^[1],[2].