Disturbance attenuation in linear systems revisited

A variety of methods have been proposed for attenuating or rejecting disturbances in linear systems. Most of the approaches, however, are targeting the performance either near resonance or across the whole frequency range. Weighting functions can be utilized to shape the frequency response function over target frequency band but they are usually of rule-of-thumb nature. A methodology is necessitated for designing controllers with performance specified at any discrete frequency or over any desired frequency band. The paper aims to develop such a methodology. Besides this, the proposed method can tell performance limitations and determine the problem of existence of optimal controllers, as well as providing a useful framework to improve the performance of an existing controller. A number of important results are obtained and these results are subsequently validated through a practical application to a rotor blade example.