Reduced-order observer based H∞ controller design for two nonstandard problems

This paper presents some methods to design the Luenberger reduced-order H_∞ compensator for two nonstandard cases. These are the design problems in which the direct feed-through matrices, from control inputs to controlled outputs and from disturbances to measured outputs, do not satisfy the standard H_∞ assumptions. In the previously developed approaches for nonstandard problems, at least one of the mentioned assumptions needs to be satisfied. The proposed approaches need to solve only one Riccati equation. The methods are developed based on the bounded real lemma. A numerical example is included to illustrate the effectiveness of the proposed technique.