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Keywords:
asymptotic stability in probability; control Lyapunov function; smooth state feedback law
asymptotic stability in probability; control Lyapunov function; smooth state feedback law
Summary:
The purpose of this paper is to provide sufficient conditions for the feedback asymptotic stabilization in probability for a class of affine in the control nonlinear stochastic differential systems. In fact, under the assumptions stated in this paper we prove the existence of a control Lyapunov function that according to the stochastic version of Artstein's theorem guarantees the asymptotic stability in probability by means of a state feedback law that is smooth except eventually at the equilibrium. This result generalizes the well-known theorem of Vidyasagar concerning the feedback stabilization problem for interconnected control systems.
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