Synchronization for coupled neural networks with interval delay: a novel augmented Lyapunov-Krasovskii functional...

Area of Science:

• Control Systems Engineering
• Computational Neuroscience
• Network Science

Background:

• Synchronization is crucial for complex systems like neural networks.
• Time-varying delays and hybrid coupling pose significant challenges to achieving synchronization.
• Existing methods often yield conservative results due to stringent conditions.

Purpose of the Study:

• To develop novel, less conservative delay-dependent synchronization criteria for neural networks with hybrid coupling and interval time-varying delay.
• To propose a robust synchronization criterion for systems with parameter uncertainties.
• To ensure the proposed criteria are easily verifiable in practice.

Main Methods:

• A novel augmented Lyapunov-Krasovskii functional (LKF) method is proposed.
• The method utilizes new augmented matrices with Kronecker product operations for relaxed conditions.
• Linear Matrix Inequality (LMI) formulations are employed for practical verification.

Main Results:

• The proposed method achieves less conservative synchronization results compared to existing approaches.
• It effectively handles interval time-varying delays, including fast variations.
• A robust synchronization criterion is derived for systems with coefficient and coupling matrix uncertainties.

Conclusions:

• The novel LKF method significantly enhances synchronization criteria for complex neural networks.
• The approach offers improved performance and reduced conservatism, applicable to systems with uncertainties and varying delays.
• The LMI-based criteria ensure practical applicability and ease of verification.