Delay-Dependent Stability for Genetic Regulatory Networks

The study of stability is essential for designing or controlling genetic regulatory networks, which can be described by nonlinear differential equations with time delays. Much attention has been paid to the study of delay-independent stability of genetic regulatory networks and as a result, many sufficient conditions have been derived for delay- independent stability. Although it might be more interested in practice, delay-dependent stability of genetic regulatory networks has been studied insufficiently. Based on linear matrix inequality (LMI) approach, in this study we will present some delay-dependent stability conditions for genetic regulatory networks. To illustrate the effectiveness of our theoretical results, a gene repressillatory network is analyzed.