Robust and Global Delay-Dependent Stability for Genetic Regulatory Networks With Parameter Uncertainties

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 interesting in practice, delay-dependent stability of genetic regulatory networks has been studied insufficiently. Based on the linear matrix inequality (LMI) approach, in this study we will present some delay-dependent stability conditions for genetic regulatory networks. Then we extend these results to genetic regulatory networks with parameter uncertainties. To illustrate the effectiveness of our theoretical results, gene repressilatory networks are analyzed.