Almost sure exponential stability of stochastic Cohen-Grossberg neural networks with Markovian jumping and impulses
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- 英文论文题名：Almost sure exponential stability of stochastic Cohen-Grossberg neural networks with Markovian jumping and impulses
- 论文作者：Yunxia Sun ; Pei Cheng ; Fengqi Yao
- 英文论文作者：Yunxia Sun ; Pei Cheng ; Fengqi Yao ; School of Mathematical Sciences ; Anhui University ; School of Electrical Engineering and Information ; Anhui University of Technology
- 年：2017
- 作者机构：School of Mathematical Sciences,Anhui University;School of Electrical Engineering and Information,Anhui University of Technology;
- 英文论文关键词：Stochastic Cohen-Grossberg neural networks ; almost sure exponential stability ; Markovian jumping ; impulses
- 会议召开时间：2017-07-26
- 会议录名称：第36届中国控制会议论文集（B）
- 英文会议录名称：Proceedings of the 36th Chinese Control Conference（B）
- 语种：英文
- 分类号：TP183
- 学会代码：KZLL
- 会议名称：第36届中国控制会议
- 会议地点：中国辽宁大连
- 主办单位：中国自动化学会控制理论专业委员会
- 学会名称：中国自动化学会控制理论专业委员会
- 页数：6
- 文件大小：211k
- 原文格式：D
- 会议级别：全国
摘要
By employing the Lyapunov function method and average impulsive interval approach, the almost sure exponential stability for stochastic Cohen-Grossberg neural networks with Markovian jumping and impulses are considered. A set of sufficient conditions of almost sure exponential stability are derived. An example is given to illustrate the effectiveness of the results obtained.
By employing the Lyapunov function method and average impulsive interval approach, the almost sure exponential stability for stochastic Cohen-Grossberg neural networks with Markovian jumping and impulses are considered. A set of sufficient conditions of almost sure exponential stability are derived. An example is given to illustrate the effectiveness of the results obtained.
By employing the Lyapunov function method and average impulsive interval approach, the almost sure exponential stability for stochastic Cohen-Grossberg neural networks with Markovian jumping and impulses are considered. A set of sufficient conditions of almost sure exponential stability are derived. An example is given to illustrate the effectiveness of the results obtained.
引文
[1]M.A.Cohen,S.Grossberg,Absolute stability of global pattern formation and parallel memory storage by competitive neural networks,IEEE Trans.Syst.Man Cybern,1983,13(5):815-826.
[2]K.L.Li,Q.K.Song,Exponential stability of impulsive stochastic Cohen-Grossberg neural networks with time-varying delays and reaction-diffusion terms,Neurocomputing,2008,72(1-3):231-240.
[3]X.L.Fu,X.D.Li,LMI conditions for stability of impulsive stochastic Cohen-Grossberg neural networks with mixed delays,Communication in Nonlinear Science and Numerical Simulation,2011,16(1):435-454.
[4]C.L.Zhang,F.Q.Deng,X.Y.Zhao,and B.Zhang,p-th exponential synchronization of Cohen-Grossberg neural networks with mixed time-varying delays,and unknown parameters using impulsive control method,Neurocomputing,2016,218:432-438.
[5]Q.X.Zhu,X.D.Li,Exponential and almost sure exponential stability of stochastic fuzzy delayed Cohen-Grossberg neural networks,Fuzzy Sets and Systems,2012,203:74-94.
[6]Y.Q.Yang,T.Liang,X.Y.Xu,Almost sure exponential stability of stochastic Cohen-Grossberg neural networks with continuous distributed delays of neutral type,Optik-International Journal for Light and Electron Optics,2015,126(23):4628-4635.
[7]P.Tino,M.Cernansky,L.Benuskova,Markovian architectural bias of recurrent neural networks,IEEE Transactions,2004,15(1):6-15.
[8]M.Dong,H.G.Zhang,and Y.C.Wang,Dynamics analysis of impulsive stochastic Cohen-Grossberg neural networks with Markovian jumping and mixed time delays,Neurocomputing,2009,72(7-9)1999-2004.
[9]R.Rakkiyappan,P.Balasubramaniam,Dynamics analysis of Markovian jumping impulsive stochastic Cohen-Grossberg neural networks with discrete and distributed time-varying delays,Nonlinear Analysis:Hybrid Systems,2009,3(4):408-417.
[10]Q.X.Zhu,J.D.Cao,Robust exponential stability of Markovian jump impulsive stochastic Cohen-Grossberg neural networks with mixed time delays,IEEE Trans.Neural Netw.2010,21(8):1314-1324.
[11]P.Cheng,L.Shang,F.Q.Yao,Exponential stability of Markovian jumping stochastic Cohen-Grossberg neural networks with mixed time delays and impulses,Proceedings of the 34th Chinese Control Conference,2015,1793-1798.
[12]J.Q.Lu,D.W.Ho,J.D.Cao,An unifed synchronization criterion for impulsive dynamical networks,Automatica 2010,46(7):1215-1221.
[13]J.P.Hespanha,D.Liberzon,A.R.Teel,Lypunov conditions for input-to-state stability of impulsive systems,Automatica,2008,44:857-869.
[14]X.Wu,Y.Tang,and W.Zhang,Input-to-state stability of impulsive stochastic delayed systems under linear assumptions,Automatica,2016,66:195-204.
[15]F.Q.Yao,J.D.Cao,P.Cheng and L.Qiu,Generalized Averge dwell time approach to stability and input-to-state stability of hybrid impulsive stochastic differential systems,Nonlinear Analysis:Hybrid Systems,2016,22:147-160.
[16]X.R.Mao,C.G.Yuan,Stochastic Differential Equations with Markovian Switching,Imperial College Press,London,2006.
[17]W.J.Anderson,Continuous-time Markov chains,New York:Springer,1991.
[2]K.L.Li,Q.K.Song,Exponential stability of impulsive stochastic Cohen-Grossberg neural networks with time-varying delays and reaction-diffusion terms,Neurocomputing,2008,72(1-3):231-240.
[3]X.L.Fu,X.D.Li,LMI conditions for stability of impulsive stochastic Cohen-Grossberg neural networks with mixed delays,Communication in Nonlinear Science and Numerical Simulation,2011,16(1):435-454.
[4]C.L.Zhang,F.Q.Deng,X.Y.Zhao,and B.Zhang,p-th exponential synchronization of Cohen-Grossberg neural networks with mixed time-varying delays,and unknown parameters using impulsive control method,Neurocomputing,2016,218:432-438.
[5]Q.X.Zhu,X.D.Li,Exponential and almost sure exponential stability of stochastic fuzzy delayed Cohen-Grossberg neural networks,Fuzzy Sets and Systems,2012,203:74-94.
[6]Y.Q.Yang,T.Liang,X.Y.Xu,Almost sure exponential stability of stochastic Cohen-Grossberg neural networks with continuous distributed delays of neutral type,Optik-International Journal for Light and Electron Optics,2015,126(23):4628-4635.
[7]P.Tino,M.Cernansky,L.Benuskova,Markovian architectural bias of recurrent neural networks,IEEE Transactions,2004,15(1):6-15.
[8]M.Dong,H.G.Zhang,and Y.C.Wang,Dynamics analysis of impulsive stochastic Cohen-Grossberg neural networks with Markovian jumping and mixed time delays,Neurocomputing,2009,72(7-9)1999-2004.
[9]R.Rakkiyappan,P.Balasubramaniam,Dynamics analysis of Markovian jumping impulsive stochastic Cohen-Grossberg neural networks with discrete and distributed time-varying delays,Nonlinear Analysis:Hybrid Systems,2009,3(4):408-417.
[10]Q.X.Zhu,J.D.Cao,Robust exponential stability of Markovian jump impulsive stochastic Cohen-Grossberg neural networks with mixed time delays,IEEE Trans.Neural Netw.2010,21(8):1314-1324.
[11]P.Cheng,L.Shang,F.Q.Yao,Exponential stability of Markovian jumping stochastic Cohen-Grossberg neural networks with mixed time delays and impulses,Proceedings of the 34th Chinese Control Conference,2015,1793-1798.
[12]J.Q.Lu,D.W.Ho,J.D.Cao,An unifed synchronization criterion for impulsive dynamical networks,Automatica 2010,46(7):1215-1221.
[13]J.P.Hespanha,D.Liberzon,A.R.Teel,Lypunov conditions for input-to-state stability of impulsive systems,Automatica,2008,44:857-869.
[14]X.Wu,Y.Tang,and W.Zhang,Input-to-state stability of impulsive stochastic delayed systems under linear assumptions,Automatica,2016,66:195-204.
[15]F.Q.Yao,J.D.Cao,P.Cheng and L.Qiu,Generalized Averge dwell time approach to stability and input-to-state stability of hybrid impulsive stochastic differential systems,Nonlinear Analysis:Hybrid Systems,2016,22:147-160.
[16]X.R.Mao,C.G.Yuan,Stochastic Differential Equations with Markovian Switching,Imperial College Press,London,2006.
[17]W.J.Anderson,Continuous-time Markov chains,New York:Springer,1991.