Fixed-Time Stability of Random Nonlinear Systems

Dear Editor, This letter embarks on an examination of fixed-time stability (FxTS) for random nonlinear systems (RNSs) governed by random differential equations. This endeavor encompasses a multifaceted analysis of FxTS, commencing with its rigorous definition and its integration with Lyapunov theory, along which a consequential corollary emerges. Particularly, the positive definiteness of the expectation of settling time is established, and a less conservative upper bound is derived. The effectiveness of the proposed fixed-time theorem is verified by an example.