4.7 Article

Continuous finite-time state feedback stabilizers for some nonlinear stochastic systems

Journal

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL
Volume 25, Issue 11, Pages 1581-1600

Publisher

WILEY
DOI: 10.1002/rnc.3161

Keywords

finite-time stabilization; adding a power integrator; stochastic Lyapunov stability; state feedback controllers; stochastic nonlinear systems

Funding

  1. Natural Science Foundation of China [61174212]

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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. Copyright (C) 2014 John Wiley & Sons, Ltd.

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