Fixed-Time Lyapunov Criteria of Stochastic Nonlinear Systems and Its Generalization

This study investigates the fixed-time stability of stochastic nonlinear systems described by Itô differential equations. The improved fixed-time Lyapunov theorem is given and an important corollary is obtained. It is proved that the upper-bound estimate of the settling time is less conservative. We establish a new definition of practically fixed-time stability in probability and propose the corresponding Lyapunov criterion theorem. In addition, different cases of the parameters are discussed to provide a less conservative upper-bound estimate of the settling time. The effectiveness of the proposed stability and controller is demonstrated by two simulation examples.