Covariance control discrete systems

Recently, a theory for the control of covariances has been introduced for continuous systems [1]. The theory satisfies two needs. First, the performance requirements of many engineering control problems are naturally stated in terms of the root-mean-squared (rms) values of the system states or outputs. A theory of covariance control could be used in the design of control laws to satisfy these objectives. Secondly, the use of covariances as a measure of performance appears in the various theories for estimation, identification, realization and model reduction. Thus, a theory for the control of covariances may aid in integrating modelling and control problems. The purpose of this paper is to introduce a theory of covariance control for discrete systems.