Improved delay-dependent stability result for neural networks with time-varying delays

Area of Science:

• Control Theory
• Artificial Intelligence
• Dynamical Systems

Background:

• Neural networks with time-varying delays present significant stability challenges.
• Existing Lyapunov-Krasovskii functional (LKF) methods may not fully exploit available system information.

Purpose of the Study:

• To develop a new LKF approach for improved stability analysis of neural networks with time-varying delays.
• To enhance the utilization of activation function information and state information within the LKF framework.

Main Methods:

• A novel Lyapunov-Krasovskii functional (LKF) is proposed, incorporating instant, delayed, and maximal delayed states.
• A new derivative estimation technique combines Wirtinger-based integral inequality and extended reciprocally convex inequality.
• Full utilization of activation function information is integrated into the LKF derivative estimation.

Main Results:

• A new stability criterion for neural networks with time-varying delays is derived.
• The proposed LKF approach demonstrates reduced conservatism compared to existing methods.
• Illustrative examples confirm the effectiveness and improved performance of the new stability result.

Conclusions:

• The novel LKF approach offers a less conservative and more effective method for stability analysis of neural networks with time-varying delays.
• The technique's ability to leverage activation function and state information contributes to its improved performance.
• This work provides a valuable tool for understanding and designing stable neural network systems.