The conditions of local controllability for linear systems with stochastic parameters

The sufficient conditions of the non-predicting controllability for linear systems $\dot x=A(f^t\omega)x+B(f^t\omega)u$, $(t,\omega,x,u)\in{\mathbb R}\times\Omega\times{\mathbb R}^n\times U$ with the stationary stochastic parameters are obtained. The control is called non-predicting if the information about system in the moment $t=\tau$ is known only for $t\leqslant\tau$. The probability of the local controllability for the system on the segment $[0,T]$ is estimated.