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This paper is concerned with the problem of finite-time stabilization for some nonlinear stochastic systems. Based on the stochastic Lyapunov theorem on finite-time stability that has been established by the authors in the paper, it is proven that Euler-type stochastic nonlinear systems can be finite-time stabilized via a family of continuous feedback controllers. Using the technique of adding a power integrator, a continuous, global state feedback controller is constructed to stabilize in finite time a large class of two-dimensional lower-triangular stochastic nonlinear systems. Also, for a class of three-dimensional lower-triangular stochastic nonlinear systems, a recursive design scheme of finite-time stabilization is given by developing the technique of adding a power integrator and constructing a continuous feedback controller. Finally, a simulation example is given to illustrate the theoretical results. . 1582J. YIN AND S. KHOO been proposed for various types of nonlinear dynamical systems in the literature (see [2][3][4][5][6][7][8][9][10][11][12] and references therein). In particular, the theory of finite-time stability for continuous autonomous systems has been established, and a Lyapunov stability theorem that investigates finite-time stability has also been presented by Bhat and Bernstein [13]. With the help of this theorem, Bhat and Bernstein [5] presented a continuous finite-time state feedback stabilizer for the translational and rotational double integrators; Hong et al. [6] constructed a class of output feedback controllers that achieve finite-time stability for the double integrator system by designing a nonlinear observer and using some results of homogenous systems in [4,14]; Huang et al. [8] proved global finite-time stabilization for higher-dimensional uncertain nonlinear systems in a lower-triangular form. Because only nonsmooth or non-Lipschitz continuous systems can have a finite-time stable property, a finite-time stable system might have better insensitivity to perturbations [3].The purpose of this paper is to develop finite-time stabilization control methods that are applicable to stochastic nonlinear systems. It is well known that the common Lyapunov theory plays an important role in stabilizing dynamical systems. Because of the connection between stochastic systems and dynamical systems, it is natural to first consider adopting control techniques that have been successfully applied to stabilize dynamical systems. It should be noted that most of existing stabilization results for stochastic nonlinear systems are based on the stochastic Lyapunov theorems on asymptotic stability in probability (see [15][16][17][18][19][20]). In these papers, the coefficients of stochastic nonlinear systems are required to satisfy the local Lipschitz condition in order to ensure uniqueness and local existence of strong solutions. However, Lemma 5.2.3 in [19] implies that almost all the sample paths of a stochastic differential equation starting from a non-zero initial state will never reach the origin su...

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This paper considers the problem of finite-time stability for stochastic nonlinear systems. A new Lyapunov theorem of stochastic finite-time stability is proposed, and an important corollary is obtained. Some comparisons with the existing results are given, and it shows that this new Lyapunov theorem not only is a generalization of classical stochastic finite-time theorem, but also reveals the important role of white-noise in finite-time stabilizing stochastic systems. In addition, multiple Lyapunov functionsbased criteria on stochastic finite-time stability are presented, which further relax the constraint of the infinitesimal generator LV . Some examples are constructed to show significant features of the proposed theorems. Finally, simulation results are presented to demonstrate the theoretical analysis.