Stability analysis of time-varying delay neural networks based on augmented double integral Lyapunov–Krasovskii functionals: a novel neuroscience technology

JOURNAL/atin/04.03/02274269-990000000-00016/figure1/v/2025-09-25T132224Z/r/image-tiff Neural networks, as the core of artificial intelligence, are prone to system instability due to their time-delay characteristics. However, existing stability analyses predominantly depend on highly conservative Lyapunov–Krasovskii functionals (LKFs) and integral inequalities, which are difficult to balance precision and efficiency. This review aims to address the stability analysis problems of time-delay neural networks by proposing a novel analytical approach based on double-integral functionals and augmented integral inequalities. The proposed method seeks to overcome the inherent conflicts between conservatism and computational complexity in conventional approaches, thereby advancing interdisciplinary innovation between neuroscience and control theory. A LKF containing more state information related to the delay based on the augmented integral inequality is constructed. Then, an appropriate augmented integral inequality is used to handle the double integral augmented LKF, thereby reducing the order of the delay-dependent LKF. Based on the above two points, a less conservative stability criterion for delay-dependent neural network systems is established. Finally, an example is introduced to illustrate the superiority of the results. Therefore, this technology provides a novel pathway for reliable control of complex neural networks. It holds promising potential for extension to cutting-edge domains such as spiking neural networks and brain-computer interfaces, thereby advancing the engineering applications of neuromorphic computing and brain-inspired intelligence. This breakthrough marks a significant milestone in the convergence of neuroscience and nonlinear control theory.