Variable Gradient Approach to Construct Lyapunov Function for Judging Stability of Non-Linear Systems

Abstract

This paper presented a regularization approach to construct Lyapunov function for judging the stability of non-linear systems. The gradient function is derived primarily from the state equation of the non-linear system. The gradient function coefficients is determined such that a negative positive derivative function of Lyapunov function is derived. Then a Lyapunov function is solved by the line integral to the gradient function. And then judging whether the solved Lyapunov function is positive definite. Application examples indicate there can construct a Lyapunov function for asymptotically stable non-linear system. This approach provides another way to judge the stability of some non-linear time-invariant systems.