Inverse problems in H∞ control theory and linear-quadratic differential games

For a given state-feedback control law, necessary (frequency domain) conditions are given for the given state feedback to be the central solution to a standard H_∞ control problem. These conditions together with some additional conditions turn out to be sufficient as well. The conditions appear to be natural extensions of the corresponding results on the inverse problem of LQ optimal control and admit an interesting graphical interpretation. Similar results are obtained for an analogous inverse problem in the theory of linear-quadratic differential games