Global and robust stability analysis of genetic regulatory networks with time-varying delays and parameter uncertainties.

The study of stability is essential for designing or controlling genetic regulatory networks. This paper addresses global and robust stability of genetic regulatory networks with time delays and parameter uncertainties. Most existing results on this issue are based on the linear matrix inequalities (LMIs) approach, which results in checking the existence of a feasible solution to high dimensional LMIs. Based on M-matrix theory, we will present several novel global stability conditions for genetic regulatory networks with time-varying and time-invariant delays. All of these stability conditions are given in terms of M-matrices, for which there are many and very easy ways to be verified. Then, we extend these results to genetic regulatory networks with time delays and parameter uncertainties. To illustrate the effectiveness of our theoretical results, several genetic regulatory networks are analyzed. Compared with existing results in the literature, we also show that our results are less conservative than existing ones with these illustrative genetic regulatory networks.