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. KEY WORDS Linear-quadratic controller design Frequency-shaped cost functionals State and control frequency weighting Robust design Optimal filtering 00 V[XO,U( * )] = [u'R(jw)u + xTQ(jw)x] dt 0 (3)
These developments are discussed, for example, in References 1-6. Different methods may be used to develop controllers with frequency weighting. For example, Reference 4 uses an approach based on augmentation of the given plant and solution of a modified time-domain problem and Reference 6 uses an approach based on spectral factorization and solution of a frequency-domain problem. The present paper employs the method of References 4 and 5 that