Assessing robust stability properties of uncertain genetic regulatory networks

Abstract

This paper investigates robust stability properties of genetic regulatory networks (GRNs) affected by uncertainty. Specifically, we consider GRNs with SUM and 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.

Robustness analysis of genetic regulatory networks affected by model uncertainty

“…3. to estimate the set of vectors u for which (7) has a globally asymptotically stable equilibrium point in…”

“…Here we present some illustrative examples with GRNs in SUM form, see also [7] for examples with other kinds of GRNs. The computations are done in Matlab with the toolbox SeDuMi.…”

“…Some examples with real GRNs illustrate the use of the proposed techniques. A preliminary version of this paper is reported in [7].…”