Abstract
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.
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