Abstract
This paper describes the covariance specification problem for the linear time-invariant state-feedback control system disturbed by a colored system noise. By definition the covariance specification problem is to find the state-feedback control with which the stationary state covariance matrix coincides with the prescribed covariance matrix. The author solved a covariance specification problem for a system disturbed by a white system noise before.
In this paper the problem is extended to a system disturbed by a colored system noise. The necessary conditions of the optimal feedback gains which make the resulting state covariance coincide with the prescribed one under the minimum control effort are derived, and a sequential substitution algorithm is given for a numerical solution.
As a numerical example the control problem of an aircraft in the atmospheric turbulence is discussed.
