LQP: Dominant output feedbacks

An output feedback matrix
F
will be said to dominate another,
\bar{F}
, if the cost for
F
is not higher for any initial condition than the cost for
\bar{F}
and if the cost is lower for some (perhaps all) initial conditions. The output feedback obtained by, for example, the Levine-Athans approach does not necessarily dominate the open-loop feedback
\bar{F} = 0
, which could be unfortunate. Algorithms are given for finding feedbacks which dominate any given stabilizing feedback.