Secondary delay-partition approach to finite-time stability analysis of delayed genetic regulatory networks with reaction-diffusion terms

This paper investigates the finite time stability analysis of delayed genetic regulatory networks (GRNs) with reaction-diffusion terms under Dirichlet boundary conditions. The time delays are bounded with lower and upper bounds, where the lower bounds can be zero or non-zero. Some new triple integral terms are constructed in the Lyapunov-Krasovskii functional (LKF) and the secondary delay partition method is utilized to obtain the less conservative stability criteria for GRNs. The integral ranges also have the corresponding divisions according to the time delays. Furthermore, the optimized integral inequalities, such as the Jensen's integral inequality, Wirtinger-type integral inequality and Gronwall inequality, are applied to handle integral terms. Finally, a numerical example is presented to demonstrate the feasibility and effectiveness of the proposed criteria. (C) 2019 Elsevier B.V. All rights reserved.