## A passive system approach to feedback stabilization of nonlinear control stochastic systems.(English)Zbl 0942.60052

Author’s abstract: The purpose of this paper is to provide sufficient conditions for asymptotic stabilization in probability of nonlinear control stochastic differential systems by means of smooth state feedback laws. In particular, we prove that, as in the case of stochastic differential systems affine in the control, one can compute stabilizing feedback laws provided the unforced stochastic differential system is Lyapunov stable in probability and some rank conditions are fulfilled. Some well-known stabilization results for stochastic differential systems affine in the control proved in the literature are extended to nonaffine nonlinear control stochastic differential systems.

### MSC:

 60H10 Stochastic ordinary differential equations (aspects of stochastic analysis) 93C10 Nonlinear systems in control theory 93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, $$L^p, l^p$$, etc.) in control theory 93D15 Stabilization of systems by feedback 93E15 Stochastic stability in control theory
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