Synthesis of Covariance Controllers on the Basis of the System Embedding Technology

A new approach to the synthesis of stochastic control systems, which is called the theory of covariance control, is set out in this paper. Its essence involves securing a prescribed steady-state value of the state covariance matrix of a linear system with the aid of feedback. The necessary and sufficient conditions of the attainability of the state covariance matrix are defined and formulas for the entire set of stabilizing covariance controllers are derived.