Asymptotic and robust stability of genetic regulatory networks with time-varying delays

Time delay plays an important role in dynamics of genetic networks and cannot be ignored in the modelling of genetic regulation due to slow biochemical reactions such as gene transcription and translation, and protein diffusion between the cytosol and nucleus. This paper presents a robust analysis approach to asymptotic stability of the delayed genetic regulatory networks (GRNs) with SUM regulatory logic in which each transcription factor acts additively to regulate a gene, i.e., the regulatory function sums over all the inputs. Time delays here are assumed to be time-varying and belong to the given intervals. Based on the Lyapunov stability theory and linear matrix inequality (LMI), sufficient conditions are given to ensure the stability of the GRNs. The obtained conditions are derived in terms of LMIs which are easy to be verified via the LMI toolbox. Illustrative examples are presented to show the effectiveness of the obtained results.