An output feedback matrix

will be said to dominate another,

, if the cost for

is not higher for any initial condition than the cost for

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

, which could be unfortunate. Algorithms are given for finding feedbacks which dominate any given stabilizing feedback.