Feedback stabilization for a chemostat with delayed output

In this paper we consider a problem of asymptotic stabilization for a chemostat, by using a feedback control law and considering a delay $\tau>0$ on its output. The presence of these delays on the outputs makes more difficult to achieve our asymptotic stabilization objectives. We build a family of feedback control laws (using the dilution rate as control variable) obtaining sufficient conditions for asymptotic stabilization, given by upper bounds for the delay (which are dependent of the feedback control law). Using some reduction techniques we show that the control problem becomes equivalent to obtain global stability conditions for the zero solution of the scalar differential delay equation: $$ \dotu(t)=-G(u(t))+F(u(t-\tau)). $