Much theoretical work exists for the use of covariance matrices in both identification and in state estimation. However, there exists no theory for the control of covariances. The need for a theory of covariance control may be argued from two points: 1) many engineering systems have performance requirements which are naturally stated in terms of root-mean-square (RMS) values of the system states or output and 2) the various theories of identification, estimation, and model reduction use covariances as a measure of performance. Hence a theory on covariance control may help unify the modeling and control problem theory is introduced for designing linear feedback controllers so that the closed-loop system achieves a specified state covariance.
