Exponential stability analysis of neural networks with a time-varying delay via a generalized Lyapunov-Krasovskii functional method

As is known to all that the Lyapunov-Krasovskii functional (LKF) method plays a significant role in deriving exponential stability criteria of neural networks with a time-varying delay. However, when the LKF method is adopted, the condition that a functional is required for a neural network with a delay varying in a delay interval is so strong that it may be hard to be satisfied and lead to a conservative criterion. Therefore, a generalized LKF method is proposed by weakening the strong condition in this paper. Then, new exponential stability criteria are derived via applying the proposed method. Finally, the effectiveness of the derived criteria is verified by two numerical examples.

Automated summary

The paper investigates the application of the Lyapunov-Krasovskii functional method in neural networks and proposes a generalized LKF method to derive new exponential stability criteria by weakening the strong condition. The effectiveness of the derived criteria is verified through two numerical examples.