Feedback stabilization for a chemostat with delayed output

Abstract

We apply basic tools of control theory to a chemostat model that describes the growth of one species of microorganisms that consume a limiting substrate. Under the assumption that available measurements of the model have fixed delay T > 0, we design a family of feedback control laws with the objective of stabilizing the limiting substrate concentration in a fixed level. Effectiveness of this control problem is equivalent to global attractivity of a family of differential delay equations. We obtain sufficient conditions (upper bound for delay T < 0 and properties of the feedback control) ensuring global attractivity and local stability. Illustrative examples are included.