Finite-time stabilization of a class of high-order stochastic nonlinear systems

This paper studies the problem of almost surely finite-time stabilization for stochastic nonlinear systems. We prove that global almost surely finite-time stabilization of stochastic nonlinear systems in triangular form can be reached by the continuous feedback control law. The proof is based on the recently proposed almost surely finite-time stability theorem in [17]. A recursive design algorithm is developed for the construction of the control. The adding an integrator technique is employed to construct the global almost surely finite-time stabilizer. Simulation example is given to illustrate the theoritical analysis.