This technical note focuses on state feedback control design of positive linear systems in continuous-time domain. The main goal is to analyze stability and performance preserving the closed-loop system positivity. In some sense, the provided results fill the literature gap by considering the H-2 performance index. Indeed, although H-infinity state feedback control design of positive systems has received remarkable attention in the recent years, we believe that, for the first time, a numerical method able to provide a local optimal solution to this class of nonconvex control problems is addressed by means of a simple (since no line search is required) convergent sequence of convex programming problems. The theory and the algorithm behavior are illustrated and evaluated by numerical examples borrowed from the recent literature.