On the closed-form model for state covariance assignment problem

In this study a closed-form innovative scheme for covariance assignment problems based on the original linear stochastic system is proposed. The closed-form of the state covariance equations is derived by converting the covariance matrix Riccati equation to a new linear deterministic vector state space system. As the main result of this study, according to the Kronecker product operator, the closed-form model of the new covariance system matrices is presented. In this study, the authors perform the covariance assignment problem, reformulated as a standard disturbance rejection problem. Since the new covariance system is linear and deterministic, all conventional and well-defined control strategies would be applied.