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There are many theories about the use of covariance matrices in both identification and state estimation. However, there exists no theory about 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 naturally stated in terms of the variances of the system states and (2) the various theories of identification, estimation, and model reduction use covariances as a measure of performance. Hence a theory of covariance control may help unify the modelling and control problem. This paper introduces a theory for designing linear feedback controllers so that the closed-loop system achieves a specified state covariance.
Hotz et al. (Wed,) studied this question.