Strictly positive real H2 controller synthesis from the viewpoint of the inverse problem

This paper deals with a design problem for such observer based controllers that are strictly positive real and simultaneously H₂ optimal. There exist somewhat restrictive sufficient conditions on LQG design weights and some kinds of numerical solutions to suboptimal versions of this problem. However, no general analytical solution has been provided to the problem so far. In this paper, we consider this problem in particular from the viewpoint of the inverse problem and provide a general analytical solution, which shows an interesting structure that is required for the strictly positive real controller to be simultaneously H₂ optimal