Exponential synchronization of delayed coupled neural networks with delay-compensatory impulsive control

Area of Science:

• Control Theory
• Computational Neuroscience
• Systems Engineering

Background:

• Exponential synchronization is crucial for coupled neural networks (CNNs).
• Existing methods struggle with delayed systems and destabilizing impulsive control.
• Impulse delays often pose challenges rather than offer solutions in network synchronization.

Purpose of the Study:

• To develop a novel delay-compensatory impulsive control strategy for delayed CNNs.
• To establish sufficient criteria for achieving globally exponential synchronization (GES).
• To overcome limitations of existing methods by utilizing impulse delays constructively.

Main Methods:

• Development of a Razumikhin-type inequality accommodating destabilizing delayed impulse gains.
• Introduction of a delay-compensatory concept highlighting two critical roles in system stability.
• Integration of impulse delays to counteract unstable dynamics caused by destabilizing gains.

Main Results:

• Sufficient criteria for GES in delayed CNNs are derived using the novel inequality and control idea.
• Impulse delays are effectively utilized to compensate for instantaneous unstable impulse dynamics.
• Relaxed constraints between system and impulsive delays, decoupling impulse intervals from system delay.

Conclusions:

• The proposed delay-compensatory impulsive control method enhances stability and synchronization performance.
• The novel approach demonstrates superior performance compared to existing methods, validated by practical applications.
• This work offers a more flexible and effective framework for synchronizing complex neural networks.