Synthesis of optimal dynamic controllers of the reduced order for nonstationary discrete stochastic linear systems

On the basis of the method of direct optimization of projection matrices, equations are obtained for a quadratic-criterion-optimal dynamic controller of the reduced order for nonstationary discrete stochastic systems in the form of the difference matrix equations of optimal projection. The suggested method can be used for synthesis of optimal nonstationary estimators of the reduced order as well as the reduction of linear system order. Generalization of the considered approach to the case of continuous nonstationary systems is complicated due to the dependence of the continuous controller equations on matrix derivatives with respect to time.