Mean-square exponential input-to-state stability of delayed Cohen-Grossberg neural networks with Markovian switching based on vector Lyapunov functions

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• 作者：Zhihong Li^a ; ^{1575388989@qq.com" class="auth_mail" title="E-mail the corresponding author} ; Lei Liu^a ; ^{liulei_hust@hhu.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; ^{liulei_hust@163.com" class="auth_mail" title="E-mail the corresponding author} ; Quanxin Zhu^b ; ^c ; ^{zqx22@126.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Exponential input-to-state stability ; Cohen&ndash ; Grossberg neural network ; Halanay inequality ; MM-matrix ; Time delay ; Markovian switching
• 刊名：Neural Networks
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：84
• 期：Complete
• 页码：39-46
• 全文大小：523 K

文摘

This paper studies the mean-square exponential input-to-state stability of delayed Cohen–Grossberg neural networks with Markovian switching. By using the vector Lyapunov function and property of lsi5" class="mathmlsrc">lass="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S089360801630096X&_mathId=si5.gif&_user=111111111&_pii=S089360801630096X&_rdoc=1&_issn=08936080&md5=3f5486f4a39f6b33a820afde8eab1396" title="Click to view the MathML source">Mlass="mathContainer hidden">lass="mathCode">low="scroll">M-matrix, two generalized Halanay inequalities are established. By means of the generalized Halanay inequalities, sufficient conditions are also obtained, which can ensure the exponential input-to-state stability of delayed Cohen–Grossberg neural networks with Markovian switching. Two numerical examples are given to illustrate the efficiency of the derived results.