  In this paper, we propose a new model reduction technique for linear
stochastic systems that builds upon knowledge filtering and utilizes optimal
Kalman filtering techniques. This new technique will reduce the dimension of
the noise disturbance and will allow any controller designed for the reduced
model to be refined into a controller for the original stochastic system, while
preserving any specification on the output. Although initially the reduced
model will be time-varying, a method will be provided with which the reduced
model can become time-invariant if it satisfies some minor technical
conditions. We present our theoretical findings with an example that supports
the proposed framework and illustrates how model reduction and controller
refinement of stochastic systems can be achieved. We finish the paper by
considering specific examples to analyze both completeness with respect to
controller synthesis and model order reduction with respect to the state.
