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

Feedback stabilization for a chemostat with delayed output

Gonzalo Robledo 1,

1. 

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

Received  October 2008 Revised  January 2009 Published  June 2009

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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