Finite-Time Stability and State-Feedback Stabilization of Output-Constrained Stochastic Nonlinear Systems
针对传统Lyapunov理论无法直接用于约束随机非线性系统的问题，提出一种基于时变增益函数的有限时间稳定性分析方法，并推广到输出约束下的状态反馈控制，仿真验证了有效性。
Traditional Lyapunov stability theory cannot directly apply to constrained stochastic nonlinear systems when using barrier Lyapunov functions due to their inherent lack of radial unboundedness. This article presents a novel approach to establishing finite-time stability for such systems by employing Lyapunov functions. The proposed stability analysis relies on a time-varying gain function that remains uniformly bounded. This approach ensures that the system achieves finite-time stability with an arbitrarily prescribed upper bound on the settling time, thereby effectively avoiding the unbounded controller gain problem. The resulting stability is further extended to the finite-time state-feedback control for strict-feedback stochastic nonlinear systems with output constraints. Simulation studies validate the effectiveness of the proposed control scheme.