Stabilization of a class of nonlinear stochastic systems (Q5906529)

The stochastic differential equation \[ dx= (Ax+ Bu+ f(x,u))dt+ g(x,u)dw \] is considered, with a certain set of conditions on \(A\), \(B\), \(f\) and \(g\). It is shown that there exists a linear feedback law \(u=Kx\) such that the resulting equation is exponentially stable in mean square. The proof is given by constructing an appropriate Lyapunov function.