A Lyapunov-type theorem is developed to design feedback-stabilizers using Wiener processes for dynamical systems that can contain non-vanishing disturbances and arbitrarily nonlinear growths in their system functions. The proposed stabilizers guarantee that the resulting closed-loop system is globally well-posed, and is globally practically ${\mathcal{K}}_{\mathrm{\infty }}$-exponentially $p$-stable, almost surely globally practically ${\mathcal{K}}_{\mathrm{\infty }}$-exponentially stable, and globally practically ${\mathcal{K}}_{\mathrm{\infty }}$-exponentially stable in probability. Examples on a highly nonlinear system and mobile robots are included to illustrate the fact that although the theory is complicated, its application is straightforward. It is shown that the developed stabilizers can be applied to stabilize dynamical systems that cannot be stabilized by existing deterministic control laws.

开发了一个 Lyapunov 型定理，用于使用维纳过程设计反馈稳定器，用于动态系统，这些系统可以包含非消失扰动和系统函数中的任意非线性增长。所提出的稳定器保证了所得到的闭环系统是全局适定的，并且实际上是全局的${\mathcal{ķ}}_{\mathrm{\infty }}$- 指数地$p$- 稳定，几乎可以肯定在全球范围内${\mathcal{ķ}}_{\mathrm{\infty }}$- 指数稳定，并且实际上是全局的${\mathcal{ķ}}_{\mathrm{\infty }}$- 概率指数稳定。包括高度非线性系统和移动机器人的示例，以说明尽管理论很复杂，但其应用却很简单。结果表明，开发的稳定器可用于稳定现有确定性控制律无法稳定的动态系统。