Improved delay-dependent asymptotic stability criteria for delayed neural networks

Area of Science:

• Control Theory
• Artificial Intelligence
• Dynamical Systems

Background:

• Neural networks are crucial for complex computations but their stability can be affected by time delays.
• Uncertain delays, both constant and time-varying, pose significant challenges in analyzing neural network stability.
• Existing methods for analyzing delayed neural networks (DNNs) can be overly conservative.

Purpose of the Study:

• To develop novel, less conservative conditions for ensuring the asymptotic stability of neural networks with uncertain delays.
• To address both constant and time-varying uncertain delays in the stability analysis of DNNs.
• To provide robust theoretical tools for the design and analysis of stable DNNs.

Main Methods:

• Integration of the discretized Lyapunov-Krasovskii functional (LKF) method.
• Application of the free-weighting matrix technique within the Leibniz-Newton formula.
• Formulation of delay-dependent sufficient conditions expressed as linear matrix inequalities (LMIs).

Main Results:

• New delay-dependent sufficient conditions for asymptotic stability of DNNs were derived.
• The proposed conditions are shown to be less conservative than existing stability criteria.
• Numerical simulations confirmed the effectiveness and improved performance of the new criteria.

Conclusions:

• The developed LMI-based conditions provide a more accurate and less conservative assessment of asymptotic stability for DNNs with uncertain delays.
• This work advances the theoretical understanding and practical analysis of stability in delayed dynamical systems.
• The findings contribute to the reliable design of neural network systems operating under uncertain time-varying conditions.