Synthesis of Strictly Positive Real H₂ Controllers with Loop Thransfer Recovery

Abstract

This paper considers a synthesis problem for such observer based controllers that are strictly positive real and H₂ optimal at the same time. We consider this problem in particular from the viewpoint of the inverse problem, and provide a parametrization of the controller, which shows an interesting coupling structure between the regulator and the observer gains. Among them, we concentrate on an weakly coupled class in this paper to have the LTR structure, which was not provided by the original result. For the class, we give conditions on design parameters for ensuring both properties, which can be independently calculated although the problem is the mixed one.