Global asymptotic stability analysis for delayed neural networks using a matrix-based quadratic convex approach

Area of Science:

• Control Theory
• Computational Neuroscience
• Applied Mathematics

Background:

• Neural networks with time-varying delays present stability challenges.
• Ensuring global asymptotic stability is crucial for reliable network function.
• Existing methods may not fully address complex delay dynamics.

Purpose of the Study:

• To develop novel criteria for global asymptotic stability in generalized neural networks.
• To analyze networks with interval time-varying delays.
• To propose a robust method applicable to static and local field neural networks.

Main Methods:

• Construction of a new Lyapunov-Krasovskii functional incorporating integral terms.
• Establishment of integral inequalities for functional derivatives.
• Application of a matrix-based quadratic convex approach.

Main Results:

• Demonstrated negative definiteness of the Lyapunov-Krasovskii functional derivative.
• Proved positive definiteness of the Lyapunov-Krasovskii functional.
• Formulated novel stability criteria for continuous and differentiable time-varying delays.

Conclusions:

• The proposed method effectively guarantees global asymptotic stability for generalized neural networks.
• The derived stability criteria are applicable under different delay conditions.
• Numerical examples validate the efficacy of the presented approach.