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Volume 2, Issue 2
Global Exponential Stability in Lagrange Sense for Delayed Memristive Neural Networks with Parameter Uncertainties

Liangchen Li, Rui Xu & Jiazhe Lin

DOI: 10.12150/jnma.2020.241

J. Nonl. Mod. Anal., 2 (2020), pp. 241-260.

Published online: 2021-04

[An open-access article; the PDF is free to any online user.]

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  • Abstract

This paper addresses the Lagrange stability of memristive neural networks with leakage delay and time-varying transmission delays as well as parameter uncertainties. Based on the theory of Filippov's solution, by using Lyapunov-Krasovskii functionals and the free-weighting matrix method, sufficient conditions in terms of linear matrix inequality (LMI) are given to ascertain the networks with different kinds of activation functions to be stable in Lagrange sense. Meanwhile the estimation of globally attractive sets is given. Finally, numerical simulations are carried out to illustrate the effectiveness of theoretical results.

  • Keywords

Memristive neural networks, Lagrange stability, Leakage delay, Uncertain parameters.

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COPYRIGHT: © Global Science Press

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@Article{JNMA-2-241, author = {Li , LiangchenXu , Rui and Lin , Jiazhe}, title = {Global Exponential Stability in Lagrange Sense for Delayed Memristive Neural Networks with Parameter Uncertainties}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2021}, volume = {2}, number = {2}, pages = {241--260}, abstract = {

This paper addresses the Lagrange stability of memristive neural networks with leakage delay and time-varying transmission delays as well as parameter uncertainties. Based on the theory of Filippov's solution, by using Lyapunov-Krasovskii functionals and the free-weighting matrix method, sufficient conditions in terms of linear matrix inequality (LMI) are given to ascertain the networks with different kinds of activation functions to be stable in Lagrange sense. Meanwhile the estimation of globally attractive sets is given. Finally, numerical simulations are carried out to illustrate the effectiveness of theoretical results.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2020.241}, url = {http://global-sci.org/intro/article_detail/jnma/18809.html} }
TY - JOUR T1 - Global Exponential Stability in Lagrange Sense for Delayed Memristive Neural Networks with Parameter Uncertainties AU - Li , Liangchen AU - Xu , Rui AU - Lin , Jiazhe JO - Journal of Nonlinear Modeling and Analysis VL - 2 SP - 241 EP - 260 PY - 2021 DA - 2021/04 SN - 2 DO - http://doi.org/10.12150/jnma.2020.241 UR - https://global-sci.org/intro/article_detail/jnma/18809.html KW - Memristive neural networks, Lagrange stability, Leakage delay, Uncertain parameters. AB -

This paper addresses the Lagrange stability of memristive neural networks with leakage delay and time-varying transmission delays as well as parameter uncertainties. Based on the theory of Filippov's solution, by using Lyapunov-Krasovskii functionals and the free-weighting matrix method, sufficient conditions in terms of linear matrix inequality (LMI) are given to ascertain the networks with different kinds of activation functions to be stable in Lagrange sense. Meanwhile the estimation of globally attractive sets is given. Finally, numerical simulations are carried out to illustrate the effectiveness of theoretical results.

Liangchen Li, Rui Xu & Jiazhe Lin. (1970). Global Exponential Stability in Lagrange Sense for Delayed Memristive Neural Networks with Parameter Uncertainties. Journal of Nonlinear Modeling and Analysis. 2 (2). 241-260. doi:10.12150/jnma.2020.241
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