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Stabilization for a Class of Stochastic Nonlinear Systems with Arbitrary Switching via the Common Lyapunov Function Method

Jian Wu*, Weisheng Chen, Jing Li, and Wenlong Ren
International Journal of Control, Automation, and Systems, vol. 11, no. 5, pp.926-937, 2013

Abstract : This paper addresses the stabilization problem for a class of stochastic nonlinear systems with arbitrary switching. Based on the simultaneous domination approach, the common Lyapunov function method and the backstepping technique, a state feedback controller and an output feedback controller are designed, respectively. The closed-loop systems are proved to be globally asymptotically stable in probability. The main advantage of the proposed control schemes is that the controllers are independent of switching signal. Two simulation examples are given to illustrate the effectiveness of the proposed control strategies.

Keyword : Arbitrary switching, common Lyapunov function, simultaneous domination, stochastic nonlinear systems.

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