A covariance control theory

There is much theory 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 outputs 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. This paper introduces a theory for designing linear feedback controllers so that the closed loop system achieves a specified state covariance.