A reduced order observer based controller design for $H_\infty$ optimization

In this note the H8 control problem with measurement feedback is investigated. It is well-known that for this problem, in general, we need controllers of the same dynamic order as the given system. However, in the case that some entries of the measurement vector are not noise-corrupted, we show that one can find dynamic compensators of a lower dynamical order. Note that this implies that the standard assumptions on the direct feedthrough matrices, as made in most papers on H8 control, are not satisfied. Our result can be derived by using reduced order observer based controllers.