New global stability conditions for genetic regulatory networks with time-varying delays

Abstract

The study of the global stability is essential for designing and controlling genetic regulatory networks. Most existing results on this issue are based on linear matrix inequality (LMI) approach, which results in checking the existence of feasible solutions to high dimensional LMIs. In our previous study, we present several stability conditions for genetic regulatory networks with time-varying delays, based on M-matrix theory and the non-smooth Lyapunov function. In this paper, we design a smooth Lyapunov function and employ M-matrix theory to derive new stability conditions for genetic regulatory networks with time-varying delays. Theoretically, these conditions are less conservative than existing ones in some cases. For genetic regulatory networks with n genes and n proteins, these conditions become to check if an n×n matrix is an M-matrix, which is much easier than existing results. To illustrate the effectiveness of our theoretical results, two genetic regulatory networks are analyzed.