Stability analysis for delayed neural networks based on the augmented Lyapunov-Krasovskii functional with delay-product-type and multiple integral terms

Abstract This paper studies the stability problem for neural networks with time-varying delay. A novel Lyapunov-Krasovskii functional (LKF) is constructed that contains a delay-product-type (DPT) functional and a multiple-integral-type (MIT) functional. Therein, the DPT functional covers some existing ones as its special cases. In order to estimate the derivative of the MIT functional, an auxiliary function-based multiple integral inequality (AFMII) is presented, which can treat some existing results as its special cases. Based on these ingredients, a novel stability condition is obtained for neural networks with time-varying delay. A numerical example is given to illustrate the advantages of the stability condition.