Stabilization and positiveness of 2-D systems by local state-feedback: An LMI approach

This paper investigates the stabilization of 2-D systems, described by the Second Fornasini-Marchesini Model, when the closed-loop is required to be positive. More precisely, a necessary and sufficient condition, expressed in terms of LMIs, is derived for the existence of controllers guaranteeing that the closed-loop system is asymptotically stable and positive, using static feedback of the local state. A numerical example is provided to illustrate that this condition makes possible to synthesize practical controllers.