LQG/LTR procedure using reduced-order Kalman filters

This paper discusses a linear-quadratic-Gaussian/loop transfer recovery (LQG/LTR) procedure using reduced-order Kalman filters by extending known exact-recovery result. The state-space realisation commonly used for reduced-order observer design is employed. The zero structure intrinsic to the realisation is revealed. Asymptotic recovery is achieved using a non-singular reduced-order Kalman filter with a parameterised set of covariance matrices. The proposed procedure provides a systematic method for directly designing reduced-order LQG controllers without additional coordinate transformations. A numerical design example for a simple multivariable plant is presented to compare the proposed design with the standard LQG/LTR design using a full-order Kalman filter.