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

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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.