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.
Citation: Gonzalo Robledo. Feedback stabilization for a chemostat with delayed output[J]. Mathematical Biosciences and Engineering, 2009, 6(3): 629-647. doi: 10.3934/mbe.2009.6.629
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
$\tau>0$, 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.