Positive bio-circuits design for nonlinear biochemical networks

This paper considers the positive bio-circuits design problem 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. It is shown that the conditions could 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 given to illustrate the validity of the obtained results.