A Jurdjevic-Quinn-type theorem for stochastic nonlinear control systems

We consider stochastic nonaffine nonlinear control systems x/sub t/=x/sub 0/+/spl int//sub 0//sup t/ f(x/sub s/,u) ds+/spl int//sub 0//sup t/ g(x/sub s/,u) d/spl omega//sub s/ (written in the sense of Ito), /spl omega/ being a standard Wiener process, for which we give a sufficient condition for global stabilization by a bounded smooth state feedback that is explicitly given. This condition generalizes the well-known Jurdjevic-Quinn result for deterministic affine control systems.