Constrained stabilization with maximum stability radius for linear continuous-time systems

This Paper considers the problem of constrained stabilization of linear continuous-time systems by state feedback control law. The goal is to solve this problem under positivity constraint which means that the resulting closed-loop systems are not only stable, but also positive. We focus on the class of linear continuous-time positive systems (Metzlerian systems) and use the interesting properties of Metzler matrix to provide the necessary ingredients for the main results of the paper. First, some necessary and sufficient conditions are presented for the existence of controllers satisfying the Metzlerian constraint, and the constrained stabilization is solved using linear programming (LP) or linear matrix inequality (LMI). A major objective is to formulate the constrained stabilization problem with the aim of maximizing the stability radius. We show how to solve this problem with an additional LMI formulation.