H∞ control with unstable weighting functions. A design method of H∞ robust servo systems

Deals with H_∞ control problems in which some of the weighting functions possibly have jω poles. Such a problem naturally arises when one deals with robust servo system designs with an H_∞-norm criterion. Special attention is paid to the class of the controllers which have the same jω poles that the weighting functions have, namely, the controllers equipped with internal models. It is shown that the: existence conditions of a controller solving the problem and the controller formulas are very similar to the well-known case where all the weighting functions are assumed to be stable: The existence conditions involve two game-type algebraic Riccati equations (ARE), and a parameterization of the controllers is given by a linear fractional transformation (LFT) on a free stable contraction. The only difference is that the solution involves quasi-stabilizing solutions of game-type ARE´s whose definition is given in this paper