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. The 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.