A characterization of solutions to the inverse H∞ optimal control problem

The paper is concerned with the inverse H_∞ optimal control problem. The inverse H_∞ optimal control is to find plants whose H_∞ optimal controller is a given controller. The paper gives a characterization of solutions to the inverse H_∞ optimal control problem. For some plants on the ´boundary´ of the set parametrized with respect to a given controller, the given controller is an H_∞ optimal controller and the optimal value is the prespecified value. In other word, such plants on the ´boundary´ of the parametrization are of the same difficulty with respect to all the possible controllers. The characterization of such plants is given in the paper