Exponential stability of neural networks with a time-varying delay via a cubic function negative-determination lemma

Xu-Kang Chang, Yong He and Zhen-Man Gao

Applied Mathematics and Computation, 2023, vol. 438, issue C

Abstract: The problem of global exponential stability of neural networks with a time-varying delay is studied in this article. Firstly, to fully utilize the cross-term relationships among state variables, an improved augmented delay-product-type Lyapunov-Krasovskii functional, including an extra double integral state, is established for the stability analysis. Accordingly, this augmented LKF derivative is a higher-order function of the time-varying delay. Then, three state vectors are considered to reduce the order of the function to cubic. So, to obtain the feasible negative-definiteness condition of this LKF derivative of non-convexity, a negative-determination lemma for cubic functions is employed to handle this problem. As a result, a novel stability criterion is obtained. Two well-known numerical examples illustrate the effectiveness of the criterion.

Keywords: Neural networks; Exponential stability; Time-varying delay; Lyapunov-Krasovskii functional; Cubic function negative-determination lemma (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:438:y:2023:i:c:s0096300322006750

DOI: 10.1016/j.amc.2022.127602

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