H∞/LTR observer based controllers: Direct and indirect design methods

This paper describes two H_∞ design methods for observer based controllers, where the controllers are required to satisfy specific loop transfer recovery (LTR) conditions. A general formulation of the LTR problem based on recovery errors is introduced along with the Q-observer based controller. The Q-observer is an implementation of the Youla (Q-) parameterization. Further, the H_∞/LTR problem is stated in two different formulations, the indirect and the direct H_∞/LTR problem. The indirect H_∞/LTR problem, which is strongly related to the LQG/LTR problem, is solved by using the singular H_∞ state-space approach due to A.A. Stoorvogel (1989) and to Stoorvogel and H.L. Trentelman (1990). Solutions to the direct H_∞/LTR problem are derived and an example comparing the two methods is presented