Journal of Applied Mathematics

Impulsive State Feedback Control of Cheese Whey Fermentation for Single-Cell Protein Production

Chunjin Wei, Shuwen Zhang, and Lansun Chen

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Abstract

The work is the analysis of a mathematical model of cheese whey fermentation for single-cell protein production with impulsive state feedback control. Through the analysis, the sufficient conditions of existence and stability of positive order-1 periodic solution are obtained. It is shown that the system either tends to a stable state or has a periodic solution, which depends on the feedback state, the control parameter of the dilution rate, and the initial concentrate of microorganism and substrate. For some special cases, it is also shown that the system may exist in order-2 periodic solution. Furthermore, our findings are confirmed by means of numerical simulations.

Article information

Source
J. Appl. Math., Volume 2013 (2013), Article ID 354095, 10 pages.

Dates
First available in Project Euclid: 14 March 2014

Permanent link to this document
https://projecteuclid.org/euclid.jam/1394808082

Digital Object Identifier
doi:10.1155/2013/354095

Mathematical Reviews number (MathSciNet)
MR3090611

Zentralblatt MATH identifier
06950631

Citation

Wei, Chunjin; Zhang, Shuwen; Chen, Lansun. Impulsive State Feedback Control of Cheese Whey Fermentation for Single-Cell Protein Production. J. Appl. Math. 2013 (2013), Article ID 354095, 10 pages. doi:10.1155/2013/354095. https://projecteuclid.org/euclid.jam/1394808082


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