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Feedback stabilization for a chemostat with delayed output
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
$\tau>0$, 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 $\tau>0$ and
properties of the feedback control) ensuring global attractivity and local
stability. Illustrative examples are included.