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Global Finite-Time Stabilization of Stochastic Nonlinear Systems with Low-Order Nonlinearities

Abstract: This paper investigates the problem of global finite-time stabilization by state feedback for a class of stochastic nonlinear systems with low-order nonlinearities, to which the existing control methods are inapplicable. By skillfully adopting the method of adding a power integrator and constructing twice continuous differential Lyapunov functions, a stepwise constructive continuous state feedback control methodology is proposed. Based on stochastic finite-time stability theorem, it is proved that the solution of the closed-loop system is finite-time stable in probability. Two simulation examples are provided to illustrate the effectiveness of the proposed approach.