Minimum energy covariance controllers

Covariance control theory provides a parametrization of all controllers which assign a specified covariance matrix to the closed loop system. Such controllers are not unique. In this paper we obtain the analytical expression for the covariance controllers which minimize the required control effort. These are solutions to a minimum/guaranteed performance control design problem, in the sense that the required control effort is minimized subject to the performance constraints guaranteed by a specified state covariance matrix assignment. In a different interpretation of the results, the solution to a minimum effort controller redesign problem is obtained. The minimum effort covariance control problem is solved for the discrete time dynamic output feedback case