Further Stability Analysis for Time-Delayed Neural Networks Based on an Augmented Lyapunov Functional

In this paper, the stability of time-delayed neural networks (DNN) is further analyzed. First, an augmented $N$ -dependent Lyapunov–Krasovskii functional (LKF) is designed, where the non-integral terms are augmented with delay-dependent items and some additional state variables, and the integrated vector in the single-integral terms is also augmented by adding some integral interval-dependent items. The novel LKF complements some coupling information between the neuron activation function and other state variables. Second, a new delay-dependent stability criterion is proposed via the above LKF application. Third, in order to further demonstrate the advantages of the new LKF, two corollaries are also given under other simplistic LKFs. Finally, some common numerical examples are presented to show the effectiveness of the proposed approach.