Feedback stabilization for a chemostat with delayed output

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

Feedback stabilization for a chemostat with delayed output

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

Received October 2008 Revised January 2009 Published June 2009

Abstract
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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.

Keywords: control theory, chemostat., differential delay equations, global stability.

Mathematics Subject Classification: Primary: 93D15, 92D25; Secondary: 34K2.

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

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