I. Introduction
When a plant has more control inputs than controlled outputs, the same output evolution can be imposed by infinitely many different choices of input evolutions. This aspect opens the door to the opportunity of performing a selection of the inputs that is optimal with respect to a certain functional of interest. Although a direct optimal control design could be performed, practical considerations often suggest to separate the design in two steps: first, a stabilizing controller is designed based e.g. on robustness considerations and other requirements, and then an add-on compensator in charge of control allocation is inserted in the previously designed closed-loop system. Such an approach has proved to be very fruitful in a variety of applications, including plasma confinement in Tokamaks [1], [2], automotive applications, as well as marine vehicles control, track following in hard disks, aircraft control, and several others: see e.g. the contributions [3]–[8], as well as the survey work [9] (and the papers in its reference list).