Stability Analysis for Delayed Neural Networks via Improved Auxiliary Polynomial-Based Functions

This brief is concerned with stability analysis for delayed neural networks (DNNs). By establishing polynomials and introducing slack variables reasonably, some improved delay-product type of auxiliary polynomial-based functions (APFs) is developed to exploit additional degrees of freedom and more i...

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Bibliographic Details
Published in:IEEE transaction on neural networks and learning systems 2019-08, Vol.30 (8), p.2562-2568
Main Authors: Li, Zhichen, Yan, Huaicheng, Zhang, Hao, Zhan, Xisheng, Huang, Congzhi
Format: Article
Language:English
Subjects:
Artificial neural networks
Auxiliary polynomial-based functions (APFs)
Delay
delay-product terms
delayed neural networks (DNNs)
Delays
Functions (mathematics)
Neural networks
Numerical stability
Polynomials
Quadratic forms
Slack variables
stability
Stability analysis
Stability criteria
Symmetric matrices
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Summary:This brief is concerned with stability analysis for delayed neural networks (DNNs). By establishing polynomials and introducing slack variables reasonably, some improved delay-product type of auxiliary polynomial-based functions (APFs) is developed to exploit additional degrees of freedom and more information on extra states. Then, by constructing Lyapunov-Krasovskii functional using APFs and integrals of quadratic forms with high order scalar functions, a novel stability criterion is derived for DNNs, in which the benefits of the improved inequalities are fully integrated and the information on delay and its derivative is well reflected. By virtue of the advantages of APFs, more desirable performance is achieved through the proposed approach, which is demonstrated by the numerical examples.
ISSN:2162-237X
2162-2388
DOI:10.1109/TNNLS.2018.2877195