Neuronal State Estimation for Neural Networks With Two Additive Time-Varying Delay Components.

Area of Science:

• Control Theory
• Artificial Neural Networks
• Systems Engineering

Background:

• Neural networks are crucial in modern control systems.
• Time-varying delays in neural networks pose significant challenges for state estimation.
• Existing methods often struggle with complex delay scenarios.

Purpose of the Study:

• To develop a robust state estimation method for neural networks with multiple time-varying delays.
• To address three distinct cases of time-varying delays: differentiable, continuous, and mixed.
• To design Luenberger estimators for guaranteed global asymptotic stability.

Main Methods:

• Introduction of an extended reciprocally convex inequality for bounding Lyapunov-Krasovskii functionals.
• Derivation of sufficient conditions tailored to the three delay cases.
• Application of a linear-matrix-inequality (LMI)-based approach with tuning parameters.

Main Results:

• Sufficient conditions for global asymptotic stability are established for all considered delay types.
• A novel Luenberger estimator design is proposed using LMIs.
• The method is successfully applied to neural networks with single interval time-varying delays.

Conclusions:

• The proposed state estimation method effectively handles complex time-varying delays in neural networks.
• The LMI-based approach provides a systematic way to design stable estimators.
• Numerical examples validate the effectiveness and robustness of the developed technique.