This paper investigates the simultaneous stabilization of a collection of continuous single‐input non‐linear stochastic systems, with coefficients that are not necessarily locally Lipschitz. A sufficient condition for the existence of a continuous simultaneously stabilizing feedback control is proposed — it is based on the generalized stochastic Lyapunov theorem and on the technique of stochastic control Lyapunov functions. This condition is also necessary, provided that the system's coefficients satisfy some regularity conditions. Moreover, the proposed feedback can be chosen to be bounded under the assumption that appropriate control Lyapunov functions are known. All the proposed simultaneously stabilizing state feedback controllers are explicitly constructed. Finally, two simulation examples are provided to demonstrate the effectiveness of the proposed approach.

中文翻译：

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单输入非线性随机系统的连续同时稳定

本文研究了连续单输入非线性随机系统集合的同时稳定，其系数不一定是局部Lipschitz。提出了存在连续同时稳定的反馈控制的充分条件-它基于广义随机Lyapunov定理和随机控制Lyapunov函数技术。只要系统的系数满足某些规律性条件，该条件也是必要的。此外，在已知适当的控制李雅普诺夫函数的假设下，可以将建议的反馈选择为有界。所有建议的同时稳定状态反馈控制器均已明确构造。最后，