Reduced-order LQG/LTR procedure for the plant output side

It is commonly believed that reduced-order observers, including reduced-order Kalman filters, cannot be used in the loop transfer recovery (LTR) design of the plant output side. In contrast to common understanding, we show that, at least for nonminimum-phase plants, the reduced-order Kalman filter can be used in the linear-quadratic-Gaussian (LQG)/LTR design of the plant output side with clear meaning in systems theory. The key concept is to regard a reduced-order Kalman filter as a high-gain full-order Kalman filter. For the reduced-order LQG controller, we examine the asymptotic property achieved by applying the recovery procedure used in the full-order LQG/LTR design. Using the equivalent full-order Kalman filter, we find that the sensitivity property of the reduced-order LQG controller is asymptotically equivalent to that of a high-gain partial output injection system. Motivated by this result, we propose the reduced-order LQG/LTR procedure taking the high-gain partial output injection system as a target. Some target properties are discussed to clarify the difference from the full-order design. A multivariable design example is presented to show that the procedure provides a systematic design of a reduced-order controller with optimality consideration.