Relaxed Stability Criteria for Neural Networks With Time-Varying Delay Using Extended Secondary Delay Partitioning and Equivalent Reciprocal Convex Combination Techniques

This article investigates global asymptotic stability for neural networks (NNs) with time-varying delay, which is differentiable and uniformly bounded, and the delay derivative exists and is upper-bounded. First, we propose the extended secondary delay partitioning technique to construct the novel L...

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Bibliographic Details
Published in:IEEE transaction on neural networks and learning systems 2020-10, Vol.31 (10), p.4157-4169
Main Authors: Wang, Shenquan, Ji, Wenchengyu, Jiang, Yulian, Liu, Derong
Format: Article
Language:English
Subjects:
Artificial neural networks
Asymptotic properties
Asymptotic stability
Automation
Delay
Delays
Equivalence
Equivalent reciprocal convex combination
extended secondary delay partitioning
global asymptotic stability
Integrals
Linear matrix inequalities
Lower bounds
Mathematical analysis
Matrix methods
Neural networks
neural networks (NNs)
Partitioning
Stability criteria
State variable
time-varying delay
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Summary:This article investigates global asymptotic stability for neural networks (NNs) with time-varying delay, which is differentiable and uniformly bounded, and the delay derivative exists and is upper-bounded. First, we propose the extended secondary delay partitioning technique to construct the novel Lyapunov-Krasovskii functional, where both single-integral and double-integral state variables are considered, while the single-integral ones are only solved by the traditional secondary delay partitioning. Second, a novel free-weight matrix equality (FWME) is presented to resolve the reciprocal convex combination problem equivalently and directly without Schur complement, which eliminates the need of positive definite matrices, and is less conservative and restrictive compared with various improved reciprocal convex inequalities. Furthermore, by the present extended secondary delay partitioning, equivalent reciprocal convex combination technique, and Bessel-Legendre inequality, two different relaxed sufficient conditions ensuring global asymptotic stability for NNs are obtained, for time-varying delays, respectively, with unknown and known lower bounds of the delay derivative. Finally, two examples are given to illustrate the superiority and effectiveness of the presented method.
ISSN:2162-237X
2162-2388
DOI:10.1109/TNNLS.2019.2952410