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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 717489, 8 pages
http://dx.doi.org/10.1155/2013/717489
Research Article

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

College of Energy and Electrical Engineering, Hohai University, Nanjing 210098, China

Received 4 February 2013; Accepted 24 March 2013

Academic Editor: Chuangxia Huang

Copyright © 2013 Yonghui Sun et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.