A linear filter in the stabilization problem for stochastic systems with incomplete information

For a controllable linear stochastic system with incomplete information conditions are obtained under which the linear filter which provides a state estimate helps solve the stabilization system. In the case of a system described by an $n$-th order equation and a single observable coordinate an algorithm for design of a stabilizing controller is indicated. Such an algorithm is proved to exist always where the system is stabilizable with complete information.