Relations between frequency dependent control and state weighting in LQG problems

The paper considers the relation between controller designs for the same linear system achieved with two different quadratic performance indices, with these indices differing only to the extent that one has frequency weighting on the control, while the other has the inverse frequency weighting on the state. The main result is that whereas the optimal controls as time functions can be the same, the optimal controllers are different. Filtering results are also obtained.