Improved Stability Criterion for Recurrent Neural Networks With Time-Varying Delays

Area of Science:

• Control Theory
• Artificial Intelligence
• Neural Networks

Background:

• Recurrent neural networks (RNNs) are crucial in modeling dynamic systems.
• Stability analysis of RNNs with time-varying delays is challenging.
• Existing methods often suffer from conservatism and complexity.

Purpose of the Study:

• To develop a new stability criterion for delay-dependent stability analysis of RNNs with time-varying delays.
• To reduce conservatism and complexity in stability analysis.
• To demonstrate the effectiveness of the proposed method.

Main Methods:

• Development of a novel augmented Lyapunov-Krasovskii functional (LKF).
• Incorporation of the nonzero lower bound of time-varying delays into the LKF.
• Utilization of integral inequality and reciprocally convex combination.
• Derivation of stability criteria within the linear matrix inequality (LMI) framework.

Main Results:

• A new, less conservative stability criterion for RNNs with time-varying delays is derived.
• The proposed LKF construction avoids using delayed state terms in augmented vectors.
• The method demonstrates reduced complexity compared to existing approaches.
• Numerical examples validate the effectiveness and superiority of the criterion.

Conclusions:

• The proposed method provides an effective and efficient approach for stability analysis of RNNs with time-varying delays.
• The developed stability criterion offers significant improvements over existing methods in terms of conservatism and complexity.
• The findings contribute to the theoretical understanding and practical application of stable recurrent neural networks.