Estimating Stable Uncertainty Sets for Genetic Regulatory Networks with Guaranteed Disturbance Attenuation

Abstract

It is well-known that models of genetic regulatory networks (GRNs) are unavoidably affected by uncertainties. This paper addresses the problem of estimating stable uncertainty sets of uncertain GRNs with guaranteed disturbance attenuation. Specifically, the GRNs are assumed to be affected by disturbances in the form of Wiener processes, and by uncertainties in the form of a parameter vector that determines the coefficients of the model via given functions. It is shown that estimates of the sought stable uncertainty sets can be obtained through a recursive strategy based on parameter-dependent Lyapunov functions and convex optimization. Some examples with fictitious and real biological models illustrate the use of the proposed strategy.