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Positive Stability Analysis and Bio‐Circuit Design for Nonlinear Biochemical Networks

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  • Yonghui Sun
  • Zhinong Wei
  • Guoqiang Sun

Abstract

This paper is concerned with positive stability analysis and bio‐circuits design for nonlinear biochemical networks. A fuzzy interpolation approach is employed to approximate nonlinear biochemical networks. Based on the Lyapunov stability theory, sufficient conditions are developed to guarantee the equilibrium points of nonlinear biochemical networks to be positive and asymptotically stable. In addition, a constrained bio‐circuits design with positive control input is also considered. It is shown that the conditions can be formulated as a solution to a convex optimization problem, which can be easily facilitated by using the Matlab LMI control toolbox. Finally, a real biochemical network model is provided to illustrate the effectiveness and validity of the obtained results.

Suggested Citation

  • Yonghui Sun & Zhinong Wei & Guoqiang Sun, 2013. "Positive Stability Analysis and Bio‐Circuit Design for Nonlinear Biochemical Networks," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:717489
    DOI: 10.1155/2013/717489
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    References listed on IDEAS

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    1. Jeff Hasty & David McMillen & J. J. Collins, 2002. "Engineered gene circuits," Nature, Nature, vol. 420(6912), pages 224-230, November.
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