Asymptotic Stability Criteria for Genetic Regulatory Networks with Time-Varying Delays and Reaction-Diffusion Terms

This paper investigates the asymptotic stability problem for delayed genetic regulatory networks with reaction-diffusion terms under both Dirichlet boundary conditions and Neumann boundary conditions. First, by constructing a new Lyapunov-Krasovskii functional and using Jensen's inequality, Wirtinger's inequality, Green's second identity and the reciprocally convex approach, we establish delay-dependent asymptotic stability criteria that do not require a restriction of the upper bounds of the delays' derivatives being less than 1. Thus, the stability criteria that we establish are less conservative than the existing criteria and extend the range of applications of the theoretical results. In addition, it is shown that the obtained criterion under Dirichlet boundary conditions retains the information about the reaction-diffusion terms, while these do not exist in the criterion under Neumann boundary conditions. It is then theoretically presented that the stability criteria established in this paper are less conservative than the existing ones. Finally, numerical examples are given to illustrate the effectiveness of the theoretical results.