Finite-Time Robust Stability of Uncertain Genetic Regulatory Networks with Time-Varying Delays and Reaction-Diffusion Terms

Abstract

This study seeks to address the finite-time robust stability of delayed genetic regulatory networks (GRNs) with uncertain parameters and reaction-diffusion terms. We employ an appropriate Lyapunov-Krasovskii functional to derive some less conservative stability criteria for GRNs under Dirichlet boundary conditions, which are delay-dependent, delay-derivative-dependent, and reaction-diffusion-dependent. The time-varying delays and their derivatives are both bounded with lower and upper bounds, where the lower bound of them can be zero or non-zero. In addition, we define some new variables to deal with uncertain parameters. Moreover, Jensen’s integral inequality, Wirtinger-type integral inequality, reciprocally convex combination inequality, Gronwall inequality, and Green formula are employed to handle integral terms. Finally, a numerical example is presented to illustrate the feasibility and effectiveness of the obtained stability criteria.