High gain observers applied to problems in disturbance attenuation, H^∞- infinity optimization and the stabilization of uncertain linear systems.

The main result of this study is an approach to the disturbance attenuation problem for the case in which some of the state variables cannot be measured. The design procedure begins with a full state-feedback design, and then the system states are reconstructed using an observer. The approach taken to design the required observer is related to the loop-transfer-recovery method. A high-gain observer is used to achieve a level of disturbance attenuation which is arbitrarily close to that which can be achieved using full state feedback. Thus, previous results on disturbance attenuation which applied only in the full state-feedback case can now be applied to a much larger class of systems. Another area in which the results of this study can be applied is the H^∞ optimization problem. It is possible to consruct a feedback compensator which achieves a bound arbitrarily close to the H^∞ optimum (provided the minimum-phase condition is satisfied).