Use of frequency dependence in linear quadratic control problems to frequency-shape robustness

Linear quadratic control problems are considered where frequency-dependent weighting on the control is assumed. When high frequencies are weighted more heavily than low frequencies, two qualitative conclusions can be drawn: passband robustness is reduced and high-frequency robustness is improved. The result gives a theoretical underpinning to the use of frequency-dependent weighting when high-frequency uncertainty is present in the plant.