Simplifying the H^∞ theory via loop shifting

The 2-Riccati H^∞ controller formulas and their derivations are simplified via various loop-shifting transformations that are naturally expressed in terms of a degree-one polynomial system matrix closely related to the Luenberger descriptor form of a system. The technique enables one, without loss of generality, to restrict attention to a simple case. Matrix fraction descriptions for the algebraic Riccati equation solutions afford another change of variables which brings the 2-Riccati H^∞ controller formulas into a cleaner, more symmetric descriptor form, with the important practical advantage that it eliminates the numerical difficulties that can occur in cases where one or both of the Riccati solutions blowup.