On the LQ feedback formulation of H∞ Output Feedback Control

It is well-known that using the standard completion of the squares (CoS) formula for the LQ regulator problem, the H∞ controller derivations and associated H∞ controller existence conditions can be directly obtained. In standard theory for general H∞ output-feedback control and in the associated software, certain preliminary “loop-shifting” transformations are needed which it turns out add unnecessarily to the complexity of the H∞ theory and to the problem of implementing the H∞ control theory in software. In this paper, we revisit the CoS derivations for the general H∞ output feedback problem without the usual assumptions or “loop-shifting” transformations. Our results demonstrate that with suitable notation the general case can be handled directly without loop shifting, thereby simplifying both the representation and the computation of general H∞ output-feedback controllers.