A Unifying Statement for an H-Infinity Optimal Controller with Positivity Properties

In this paper, we unify two already published results on state feedback H-infinity optimality. Previously, optimality has been shown for a particular controller structure in the case that the open-loop state matrix is symmetric, as well as in the case that the closed-loop system is internally positive. By contrast, the main result of the present paper gives optimality based on neither of these two properties. As a result, when applied to a class of buffer networks, it succeeds not only in showing optimality when the system parameters are chosen so as to give open-loop symmetry and closed-loop positivity, respectively, but also when both of these properties are absent.