Positive control for global stabilization of predator-prey systems

In this paper we propose a positive linear control law for the stabilization of positive equilibria in predator-prey systems. This problem is motivated by the introduction, which is by essence positive, of predators in biological control applications, to prevent excessive levels of prey (pests). We build a linear controller that we saturate at zero and prove, under some conditions, the global asymptotic stability of the equilibrium. Without one of these conditions, the point is shown to be globally attractive but may be unstable.