This paper solves finite-time stabilization problem of stochastic low-order nonlinear systems with time-varying orders and stochastic inverse dynamics. Due to stochastic low-order systems being merely continuous but not smooth, and the appearance of time-varying orders and stochastic inverse dynamics, all of control methods of stochastic nonlinear systems are inapplicable. By characterizing unmeasured stochastic inverse dynamics with finite-time stochastic input-to-state stability (FT-SISS) and applying more general stochastic finite-time stability theory, a new design and analysis method is proposed to guarantee almost sure boundedness of all the closed-loop signals and stochastic finite-time stability of stochastic low-order nonlinear systems with time-varying orders and FT-SISS inverse dynamics.

解决了具有时变阶数和随机逆动力学的随机低阶非线性系统的有限时间稳定问题。由于随机的低阶系统只是连续的而不是光滑的，并且时变阶数和随机逆动力学的出现，使得随机非线性系统的所有控制方法都不适用。通过用有限时间随机输入至状态稳定性（FT-SISS）表征不可测的随机逆动力学，并应用更通用的随机有限时间稳定性理论，提出了一种新的设计和分析方法，以保证几乎所有封闭状态的有界性具有时变阶和FT-SISS逆动力学的随机低阶非线性系统的随机环路信号和随机有限时间稳定性。