The resolution of the equation XA+XBX=HX and the pole assignment problem: A general approach

In this paper, we generalize an existing technique which is relevant to a pole placement problem and state feedback control design with constraints on control inputs. The existing technique concerns only a restrictive class of systems for which many assumptions should be satisfied. The generalization aims then at avoiding those assumptions. The advantages of generalizing this technique are to determine linear feedback controllers that asymptotically stabilize a wide class of systems which are subject to input constraints without violating these constraints, to derive a simple formula for the state feedback and to assign the whole spectrum when stable poles are not suitably located for performances. Moreover, there will be no need to assume a lack of overlap between open and closed-loop spectra. Illustrative examples are presented to point out these advantages.