Abstract
This paper considers the problem of designing a linear functional filter (L. F. F.) to estimate a linear function of the state variables of a linear stochastic system, for the purpose of implementing a feedback control law.
The L. F. F. is a linear unbiased filter, and is generally of lower order than the Kalman-Bucy filter. It is shown here that, when the L. F. F. is used in the standard LQG control problem, separation property is established for the cost and the stability. For the steady-state case, the minimal order, canonical forms and the optimal design are obtained by a single L. F. F. which estimates a scalar-valued linear function of the state. Finally, an illustrative example is given to show the effectiveness of the L. F. F..
