Exponentially Synchronous Results for Delayed Neural Networks With Leakage Delay via Switched Delay Idea and AED-ADT...

Area of Science:

• Control Theory
• Computational Neuroscience
• Systems Engineering

Background:

• Time delays significantly degrade neural network (NN) performance.
• Dynamic analysis of NNs with time delays is a critical research area.
• Existing switched systems often lack delay-dependent switching modes.

Purpose of the Study:

• Investigate exponential synchronization in switched delayed NNs with leakage term time delays.
• Develop novel methods for systems where switching modes depend on time delays.
• Analyze systems with and without state-feedback controllers.

Main Methods:

• Reconstruction of NN models into a switched form using switched delay.
• Admissible Edge-Dependent Average Dwell Time (AED-ADT) method.
• Delay-dependent switching adjustment indicators.
• Generalized delay-mode-dependent multiple Lyapunov-Krasovskii functionals (MLKFs).

Main Results:

• Novel exponential synchronization criteria derived.
• Effective switching laws presented.
• Analysis accommodates increasing Lyapunov-Krasovskii functionals during subsystem activation.
• Theoretical results verified through examples.

Conclusions:

• The proposed methods effectively achieve exponential synchronization in switched delayed NNs.
• The delay-dependent approach offers robust control strategies.
• The findings advance the understanding and application of NNs in dynamic systems.