LQ approach to an “all-solutions” formula for H∞ output feedback control

An “all-solutions” extension to the LQ-feedback formulation of H_∞ output feedback control is presented in this paper. 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. In standard theory for general H_∞ output-feedback control and in the associated software, certain preliminary “loop-shifting” transformations are needed. These add unnecessarily to the complexity of the H_∞ theory and its implementation 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 to arrive at an “all-solutions” output feedback formulation.