Mathematical Biosciences and Engineering, 2009, 6(3): 629-647. doi: 10.3934/mbe.2009.6.629.

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Feedback stabilization for a chemostat with delayed output

1. Faculty of Mechanical Engineering, Technion Israel Institute of Technology, Haifa, 32000

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.
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Keywords control theory; chemostat.; differential delay equations; global stability

Citation: Gonzalo Robledo. Feedback stabilization for a chemostat with delayed output. Mathematical Biosciences and Engineering, 2009, 6(3): 629-647. doi: 10.3934/mbe.2009.6.629

 

This article has been cited by

  • 1. Frédéric Mazenc, Zhong-Ping Jiang, Global Output Feedback Stabilization of a Chemostat With an Arbitrary Number of Species, IEEE Transactions on Automatic Control, 2010, 55, 11, 2570, 10.1109/TAC.2010.2060246
  • 2. Frédéric Mazenc, Michael Malisoff, Stability and stabilization for models of chemostats with multiple limiting substrates, Journal of Biological Dynamics, 2012, 6, 2, 612, 10.1080/17513758.2012.663795

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