Finite-time state feedback stabilization for a class of stochastic nonlinear systems

In this paper, the problem of global finite-time stabilization by state feedback for a class of continuous but non-smooth 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 globally asymptotically stable in probability (FGSP). Further, the simulation result verifies the validity of the designed controller.