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Open AccessArticle

A Delay-Dividing Approach to Robust Stability of Uncertain Stochastic Complex-Valued Hopfield Delayed Neural Networks

1
Research Center in Mathematics and Applied Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
2
Department of Mathematics, Faculty of Science, Maejo University, Chiang Mai 50290, Thailand
3
Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang mod, Thung Khru 10140, Thailand
4
Department of Science and Humanities, Vel Tech High Tech Dr. Rangarajan Dr. Sakunthala Engineering College, Avadi, Tamil Nadu 600062, India
5
Institute for Intelligent Systems Research and Innovation, Deakin University, Waurn Ponds, VIC 3216, Australia
*
Author to whom correspondence should be addressed.
Symmetry 2020, 12(5), 683; https://doi.org/10.3390/sym12050683
Received: 18 February 2020 / Revised: 12 March 2020 / Accepted: 8 April 2020 / Published: 25 April 2020
(This article belongs to the Special Issue Symmetry in Nonlinear Studies)
In scientific disciplines and other engineering applications, most of the systems refer to uncertainties, because when modeling physical systems the uncertain parameters are unavoidable. In view of this, it is important to investigate dynamical systems with uncertain parameters. In the present study, a delay-dividing approach is devised to study the robust stability issue of uncertain neural networks. Specifically, the uncertain stochastic complex-valued Hopfield neural network (USCVHNN) with time delay is investigated. Here, the uncertainties of the system parameters are norm-bounded. Based on the Lyapunov mathematical approach and homeomorphism principle, the sufficient conditions for the global asymptotic stability of USCVHNN are derived. To perform this derivation, we divide a complex-valued neural network (CVNN) into two parts, namely real and imaginary, using the delay-dividing approach. All the criteria are expressed by exploiting the linear matrix inequalities (LMIs). Based on two examples, we obtain good theoretical results that ascertain the usefulness of the proposed delay-dividing approach for the USCVHNN model. View Full-Text
Keywords: complex-valued Hopfield neural networks; robust stability; parameter uncertainties; stochastic effects complex-valued Hopfield neural networks; robust stability; parameter uncertainties; stochastic effects
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MDPI and ACS Style

Chanthorn, P.; Rajchakit, G.; Humphries, U.; Kaewmesri, P.; Sriraman, R.; Lim, C.P. A Delay-Dividing Approach to Robust Stability of Uncertain Stochastic Complex-Valued Hopfield Delayed Neural Networks. Symmetry 2020, 12, 683.

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