Relations between frequency-dependent control and state weighting in LQG problems

Abstract

This paper considers the relation between controller designs for the same linear system achieved with two different quadratic performance indices. These indices differ only to the extent that one has frequency weighting on the control whereas the other has the inverse frequency weighting on the state. The feedback controllers are constructed by augmenting the given plant and by solving a modified LQG problem for the augmented system. 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.