Assessing robust stability properties of uncertain genetic regulatory networks

This paper investigates robust stability properties of genetic regulatory networks (GRNs) affected by uncertainty. Specifically, we consider GRNs with SUMand PROD regulatory functions, where the coefficients are affected polynomially by unknown parameters constrained in a polytope, and where the saturation functions are not exactly known. It is shown that a condition for ensuring that the GRN has a globally asymptotically stable equilibrium point for all admissible uncertainties can be obtained in terms of a convex optimization problem with linear matrix inequalities (LMIs). Moreover, it is shown that a lower bound of the worst-case convergence rate of the trajectories to the equilibrium point over all the admissible uncertainties can be computed by solving a quasi-convex optimization problem with LMIs. The proposed techniques are illustrated by some numerical examples.