Are All Full-Order Dynamic Compensators Observer Based? [Lecture Notes]

Linear-quadratic-Gaussian (LQG) control theory states that the optimal compensator for a linear plant with white, Gaussian process and sensor noise and with suitable stabilizability and detectability assumptions is given by an observer-based compensator. The observer-based structure of the compensator reflects the separation principle, wherein an optimal state estimate is fed back by an optimal static full-state-feedback control law and where the observer and regulator gains are determined independently [1]-[3]. This result implies that every full-order dynamic compensator that is not observer based must be suboptimal in the sense of LQG control.