MEAN SQUARE STABILITY AND CONTROL FOR INVARIANT
MANIFOLDS OF NONLINEAR STOCHASTIC SYSTEMS
A mean square stability for the invariant manifolds
of nonlinear stochastic systems is considered. The first approximation linear systems for invariant manifolds are introduced and a notion of $P$-stability projective) is proposed. A criterion for $P$-stability is
obtained. Mean square stabilization of periodic and quasiperiodic solutions of stochastically forced nonlinear systems is considered. The necessary and sufficient stabilizability conditions are presented. The methods for design of feedback stabilizing regulator for SDEs are suggested. The examples of constructive solving of stochastic control problem are demonstrated.
Partially supported by the RFBR grants (06-01-00625, 06-08-00396)