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

Area of Science:

• Control Theory
• Computational Neuroscience
• Systems Engineering

Background:

• Neural networks are crucial in various applications.
• Time-varying delays can destabilize neural network performance.
• Stability analysis is essential for reliable neural network operation.

Purpose of the Study:

• To develop improved methods for analyzing the asymptotic stability of neural networks with time-varying delays.
• To propose a new class of Lyapunov functionals for enhanced analysis.
• To derive less conservative stability criteria.

Main Methods:

• A novel Lyapunov functional incorporating neuron activation function information.
• The delay-partitioning method.
• The reciprocally convex technique.
• Formulation of stability criteria in linear matrix inequalities (LMIs).

Main Results:

• New, less conservative delay-dependent asymptotic stability criteria for neural networks.
• The proposed method demonstrates improved analytical outcomes.
• Effectiveness validated through two numerical examples.

Conclusions:

• The developed Lyapunov functional and associated techniques provide a more effective approach to stability analysis.
• The derived linear matrix inequality (LMI) criteria offer significant improvements over existing methods.
• The findings contribute to the robust design and application of neural networks.