High gain observers applied to problems in the stabilization of uncertain linear systems, disturbance attenuation and N ∞ optimization

In recent years, a number of approaches have been developed for solving the following problem in linear systems theory: design a state feedback control so that the norm of a specified transfer function is less than a given bound over all frequencies. This paper deals with the case in which not all systems states can be measured. It shows that if a certain minimum phase condition is satisfied, then the transfer function bound achievable using state feedback can be asymptotically recovered using a high gain observer. These results have application to the problems of disturbance attenuation, H ∞ optimization and the stabilization of uncertain linear systems.