Exponential stability of stochastic neural networks with both markovian jump parameters and mixed time delays

IEEE Transactions on Systems, Man, and Cybernetics. Part B, Cybernetics : a Publication of the IEEE Systems, Man, and Cybernetics Society
Quanxin Zhu, Jinde Cao

Abstract

In this paper, the problem of exponential stability is investigated for a class of stochastic neural networks with both Markovian jump parameters and mixed time delays. The jumping parameters are modeled as a continuous-time finite-state Markov chain. Based on a Lyapunov-Krasovskii functional and the stochastic analysis theory, a linear matrix inequality (LMI) approach is developed to derive some novel sufficient conditions, which guarantee the exponential stability of the equilibrium point in the mean square. The proposed LMI-based criteria are quite general since many factors, such as noise perturbations, Markovian jump parameters, and mixed time delays, are considered. In particular, the mixed time delays in this paper synchronously consist of constant, time-varying, and distributed delays, which are more general than those discussed in the previous literature. In the latter, either constant and distributed delays or time-varying and distributed delays are only included. Therefore, the results obtained in this paper generalize and improve those given in the previous literature. Two numerical examples are provided to show the effectiveness of the theoretical results and demonstrate that the stability criteria used in the earl...Continue Reading

References

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Citations

Nov 6, 2012·Neural Networks : the Official Journal of the International Neural Network Society·He HuangXiaoping Chen
Dec 30, 2014·IEEE Transactions on Neural Networks and Learning Systems·Wenbing ZhangQingying Miao
Jun 13, 2013·IEEE Transactions on Cybernetics·Qian MaShengyuan Xu
Jun 13, 2013·IEEE Transactions on Cybernetics·Zheng-Guang WuJian Chu
Aug 17, 2011·IEEE Transactions on Neural Networks·Zheng-Guang WuJian Chu
Mar 1, 2012·IEEE Transactions on Neural Networks and Learning Systems·Quanxin Zhu, Jinde Cao
Jan 1, 2012·IEEE Transactions on Neural Networks and Learning Systems·Xinsong YangJianquan Lu
May 28, 2013·Neural Networks : the Official Journal of the International Neural Network Society·He HuangXiaoping Chen
Aug 11, 2015·IEEE Transactions on Neural Networks and Learning Systems·Xiao LiangRuili Wang
Sep 19, 2016·Neural Networks : the Official Journal of the International Neural Network Society·Zhihong LiQuanxin Zhu
Mar 26, 2011·IEEE Transactions on Systems, Man, and Cybernetics. Part B, Cybernetics : a Publication of the IEEE Systems, Man, and Cybernetics Society·Feng Lin, Hao Ying
Jul 22, 2020·Neural Networks : the Official Journal of the International Neural Network Society·Xia ZhouMinvydas Ragulskis

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