Stability analysis of delayed neural networks via improved negative definite conditions

Xiao-Gui Liu; Xiang-Jie Zhou; Min-Hai Zhang; Xin Zhou; Xiao-Gui Liu; Xiang-Jie Zhou; Min-Hai Zhang; Xin Zhou

doi:10.3934/era.2025287

Electronic Research Archive

2025, Volume 33, Issue 10: 6514-6532. doi: 10.3934/era.2025287

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Research article

Stability analysis of delayed neural networks via improved negative definite conditions

1.
Hunan High Speed Railway Operation Safety Assurance Engineering Technology Research Center, Zhuzhou 412006, China
2.
School of Railway Power Supply and Electrical Engineering, Hunan Vocational College of Railway Technology, Zhuzhou 412006, China
3.
College of Science, Hunan University of Technology, Zhuzhou 412007, China

Received: 17 August 2025 Revised: 27 September 2025 Accepted: 09 October 2025 Published: 30 October 2025

This article discusses the issue of delay-dependent stability in generalized neural networks (GNNs). First, a suitable Lyapunov-Krasovskii functional (LKF), including more state information on time delays, was constructed, effectively reducing the system's conservatism. Second, a novel stability condition was established by utilizing the suitable LKF and the matrix-valued cubic polynomials to determine the negative definite conditions. Finally, the experimental simulation results were validated using three typical numerical examples. The experimental results demonstrated the efficiency and merits of our proposed approach compared with the existing methods.
- stability condition,
- neural networks,
- linear matrix inequality (LMI),
- polynomial inequalities,
- negative definite conditions
Citation: Xiao-Gui Liu, Xiang-Jie Zhou, Min-Hai Zhang, Xin Zhou. Stability analysis of delayed neural networks via improved negative definite conditions[J]. Electronic Research Archive, 2025, 33(10): 6514-6532. doi: 10.3934/era.2025287

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Abstract

This article discusses the issue of delay-dependent stability in generalized neural networks (GNNs). First, a suitable Lyapunov-Krasovskii functional (LKF), including more state information on time delays, was constructed, effectively reducing the system's conservatism. Second, a novel stability condition was established by utilizing the suitable LKF and the matrix-valued cubic polynomials to determine the negative definite conditions. Finally, the experimental simulation results were validated using three typical numerical examples. The experimental results demonstrated the efficiency and merits of our proposed approach compared with the existing methods.

References

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