一类分数阶时滞神经网络的Lyapunov稳定性判据Lyapunov Stability Criteria of a Class of Fractional-order Delayed Neural Networks
蔡克珍,张海
摘要(Abstract):
本文主要讨论了一类Riemann-Liouville分数阶时滞神经网络的渐近稳定性。通过构造一个适当的泛函推导出Lyapunov意义下的渐近稳定性判据,该方法避免了计算Lyapunov泛函的分数阶导数,所得结果描述为矩阵不等式,并给出了一个数值例子来说明所得结果的有效性和可行性。
关键词(KeyWords): 渐近稳定性;时滞神经网络;Lyapunov泛函;Riemann-Liouville分数阶导数
基金项目(Foundation): 安徽省高校优秀青年拔尖人才支持计划重点项目(gxyqZD2016205);; 安徽省自然科学基金项目(1608085MA14);; 安徽省教育厅自然科学研究重点项目(KJ2015A152)
作者(Author): 蔡克珍,张海
DOI: 10.13757/j.cnki.cn34-1328/n.2018.02.004
参考文献(References):
- [1]MILLER K S,ROSS B.An introduction to the fractional calculus and fractional differential equations[M].New York:John Wiley&Sons,1993:44-229.
- [2]PODLUBNY I.Fractional differential equations[M].Kosice:Academic Press,1999:1-220.
- [3]KILBAS A A.SRIVASTAVA H M.TRUJILLO J J.Theory and applications of fractional differential equations[M].Amsterdam:Elsevier Science BV,2006:1-205.
- [4]LI C P,DENG W H.Remarks on fractional derivatives[J].Appl Math Comput,2007,187(2):777-784.
- [5]LIU Y.On piecewise continuous solutions of higher order impulsive fractional differential equations and applications[J].Appl Math Comput,2016,s287-288(C):38-49.
- [6]WANG J R,LV L L,ZHOU Y.New concepts and results in stability of fractional differential equations[J].Commun Nonlinear Sci Numer Simul,2012,17(6):2530-2538.
- [7]CHEN J J,ZENG Z G,JIANG P.Global mittag-leffler stability and synchronization of memristor-based fractional-order neural networks[J].Neural Networks,2014,51(3):1.
- [8]LI H L,JIANG Y L,WANG Z,ZHANG L,et al.Global MittagLeffler stability of coupled system of fractional-order differential equations on network[J].Appl Math Comput,2015,270:269-277.
- [9]REN F L,CAO F,CAO J.Mittag-Leffler stability and generalized Mittag-Leffler stability of fractional-order gene regulatory networks[J].Neurocomputing,2015,160:185-190.
- [10]LIU S,JIANG W,LI X,et al.Lyapunov stability analysis of fractional nonlinear systems[J].Appl Math Lett,2016,51:13-19.
扩展功能
本文信息
服务与反馈
本文关键词相关文章
本文作者相关文章
中国知网
分享