研究一类连续但非光滑的随机非线性系统的全局有限时间状态反馈镇定控制问题. 通过增加幂次积分器技术和四次Lyapunov函数的构造, 系统地给出了系统状态反馈有限时间镇定控制器的设计方法. 基于引入的随机非线性系统有限时间稳定的判定准则, 可以证明闭环系统的有限时间稳定性. 仿真结果进一步验证了所设计控制器的有效性.

In this paper, the problem of global finite-time stabilization by state feedback for a class of continuous but nonsmooth stochastic nonlinear systems is studied. By extending the adding-a-power-integrator technique and constructing quartic Lyapunov function, the state feedback finite time stabilization controller is designed systematically. Based on the criterion on finite time stability of stochastic systems, the closed loop system can be proved to be finite time stable. Further, the simulation result verifies the validity of the designed controller.