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Stabilization of a class of nonlinear stochastic systems. (English) Zbl 0809.93063

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.
Reviewer: L.Arnold (Bremen)

MSC:

93E15 Stochastic stability in control theory
93D30 Lyapunov and storage functions
93E03 Stochastic systems in control theory (general)
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