Abstract
We consider a particular type of LQ control problem, in which the control power is excluded from the cost function and state-observation noise is assumed. Our goal is a state feedback law that minimizes the state covariance matrix. A necessary and sufficient condition is found for a static feedback law to be optimal among all the dynamic state feedback laws. The condition is stated in terms of an algebraic Riccati equation, which is different from that appearing in the usual LQ control.
