Abstract
The aim of this work is to prove that if the equilibrium solution of a nonlinear control stochastic system is locally asymptotically stable in probability by means of a continuous state feedback law, then the resulting stochastic system obtained by adding an integrator is also locally asymptotically stable in probability by means of a smooth, except possibly at the equilibrium solution, state feedback law. This result extends to the stabilization of stochastic systems a result proved by Tsinias [9] for deterministic systems. In our proof, we make use of the stochastic version of Artstein's theorem established in [4]
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