This report discusses different approaches to stable H infinity controller design applied to the problem of augmenting the longitudinal dynamics of an aircraft. Stability of the H infinity controller is investigated by analyzing the effects of changes in the performance index weights, and modifications in the measured outputs. The existence of a stable suboptimal controller is also investigated. It is shown that this is equivalent to finding a stable controller, whose infinity norm is less than a specified bound, for an unstable plant which is determined from parametrization of all H infinity controllers. Examples are given for a gust alleviation and a command tracking problem. Oezbay, Hitay and Garg, Sanjay Glenn Research Center...