Feedback control for competition models with mortality in the chemostat

We consider feedback control for a model of competition in a chemostat with one single substrate and two species. De Leenheer and Smith studied the competition in the chemostat in the framework of feedback control theory, giving sufficient conditions for the convergence of the species toward a unique stable critical point thus avoiding the competitive exclusion. Nevertheless, they suppose that the mortality rates can be neglected. In this paper we allow non-zero mortality rates and obtain sufficient conditions for the convergence of competing species toward a unique stable critical point