On the observer based structure of covariance controllers

The problem of finding the set of all stabilizing full order controllers is equivalent to a problem of finding all matrices which can be assigned to the closed loop system as a state covariance. Necessary and sufficient conditions for a given matrix to be assignable as a covariance are given, and all controllers (of plant order) which assign a specified covariance are parametrized explicitly. The structure of covariance controllers is shown for the first time to be observer based (state estimator plus estimated-state feedback). The “central” state estimator of the covariance controller is shown to be the Kalman filter. Unlike the traditional estimator-based controller, the separation principle does not hold, but one can design a controller by assigning the estimation error covariance and the plant state covariance simultaneously