Global exponential stability of impulsive fuzzy Cohen-Grossberg neural networks with mixed delays and reaction-diffusion terms

This paper is concerned with the problem of exponential stability for a class of impulsive fuzzy Cohen-Grossberg neural networks with mixed time delays and reaction-diffusion. The mixed delays include time-varying delays and continuously distributed delays. Based on the Lyapunov method, Poincare Integral Inequality, and the linear matrix inequality (LMI) approach, we found some new sufficient conditions ensuring the global exponential stability of equilibrium point for impulsive fuzzy Cohen-Grossberg neural networks with mixed time delays and reaction-diffusion terms. These global exponential stability conditions depend on the reaction-diffusion terms and time delays. The results presented in this paper are less conservative than the existing sufficient stability conditions. Finally, some examples are given to show the effectiveness and superiority of the theoretical results.

[1]  Jinde Cao,et al.  Robust Exponential Stability of Markovian Jump Impulsive Stochastic Cohen-Grossberg Neural Networks With Mixed Time Delays , 2010, IEEE Transactions on Neural Networks.

[2]  R. Rakkiyappan,et al.  Existence, uniqueness and stability analysis of recurrent neural networks with time delay in the leakage term under impulsive perturbations , 2010 .

[3]  Ta-lun Yang,et al.  The global stability of fuzzy cellular neural network , 1996 .

[4]  Huijun Gao,et al.  New Passivity Analysis for Neural Networks With Discrete and Distributed Delays , 2010, IEEE Transactions on Neural Networks.

[5]  Jinde Cao,et al.  Impulsive Effects on Stability of Fuzzy Cohen–Grossberg Neural Networks With Time-Varying Delays , 2007, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[6]  Zidong Wang,et al.  Global exponential stability of generalized recurrent neural networks with discrete and distributed delays , 2006, Neural Networks.

[7]  Bing Chen,et al.  Robust Stability for Uncertain Delayed Fuzzy Hopfield Neural Networks With Markovian Jumping Parameters , 2009, IEEE Trans. Syst. Man Cybern. Part B.

[8]  Huaguang Zhang,et al.  Global Asymptotic Stability of Reaction–Diffusion Cohen–Grossberg Neural Networks With Continuously Distributed Delays , 2010, IEEE Transactions on Neural Networks.

[9]  Jun-Guo Lu,et al.  Robust Global Exponential Stability for Interval Reaction–Diffusion Hopfield Neural Networks With Distributed Delays , 2007, IEEE Transactions on Circuits and Systems II: Express Briefs.

[10]  Kelin Li,et al.  Stability analysis of impulsive fuzzy cellular neural networks with distributed delays and reaction-diffusion terms , 2009 .

[11]  Jinxian Li,et al.  Dynamical analysis of Cohen-Grossberg neural networks with time-delays and impulses , 2009, Neurocomputing.

[12]  Jun-Guo Lu,et al.  Global exponential stability of impulsive Cohen–Grossberg neural networks with continuously distributed delays , 2009 .

[13]  Junguo Lu.  Global exponential stability and periodicity of reaction–diffusion delayed recurrent neural networks with Dirichlet boundary conditions , 2008 .

[14]  Y. Wang,et al.  Stability Analysis of Markovian Jumping Stochastic Cohen–Grossberg Neural Networks With Mixed Time Delays , 2008, IEEE Transactions on Neural Networks.

[15]  Jinde Cao,et al.  On pth moment exponential stability of stochastic Cohen-Grossberg neural networks with time-varying delays , 2010, Neurocomputing.

[16]  Guanrong Chen,et al.  LMI-based approach for asymptotically stability analysis of delayed neural networks , 2002 .

[17]  T. Liao,et al.  Globally exponential stability of generalized Cohen–Grossberg neural networks with delays , 2003 .

[18]  Tianping Chen,et al.  Robust global exponential stability of Cohen-Grossberg neural networks with time delays , 2004, IEEE Transactions on Neural Networks.

[19]  Daoyi Xu,et al.  Global exponential stability of impulsive fuzzy cellular neural networks with mixed delays and reaction-diffusion terms , 2009 .

[20]  Jinde Cao,et al.  Global asymptotic stability of a general class of recurrent neural networks with time-varying delays , 2003 .

[21]  Jianhua Sun,et al.  Convergence dynamics of stochastic reaction–diffusion recurrent neural networks with continuously distributed delays☆ , 2008 .

[22]  Daoyi Xu,et al.  Impulsive delay differential inequality and stability of neural networks , 2005 .

[23]  Xinzhi Liu,et al.  Stability criteria for impulsive reaction-diffusion Cohen-Grossberg neural networks with time-varying delays , 2010, Math. Comput. Model..

[24]  Zhidong Teng,et al.  Impulsive Control and Synchronization for Delayed Neural Networks With Reaction–Diffusion Terms , 2010, IEEE Transactions on Neural Networks.

[25]  J. Ruan,et al.  Global stability analysis of impulsive Cohen–Grossberg neural networks with delay , 2005 .

[26]  Zidong Wang,et al.  Exponential stability of delayed recurrent neural networks with Markovian jumping parameters , 2006 .

[27]  J. Ruan,et al.  Global dynamic analysis of general Cohen–Grossberg neural networks with impulse , 2007 .

[29]  Qing Zhu,et al.  Stability analysis on Cohen–Grossberg neural networks with both time-varying and continuously distributed delays☆ , 2009 .

[30]  Zidong Wang,et al.  Stability analysis of impulsive stochastic Cohen–Grossberg neural networks with mixed time delays , 2008 .

[31]  Wei Wu,et al.  Analysis on global exponential robust stability of reaction–diffusion neural networks with S-type distributed delays , 2008 .

[32]  Xuyang Lou,et al.  Boundedness and exponential stability for nonautonomous cellular neural networks with reaction–diffusion terms , 2007 .

[33]  Guanrong Chen,et al.  On delayed impulsive Hopfield neural networks , 1999, Neural Networks.

[34]  Kelin Li,et al.  Exponential stability of impulsive Cohen-Grossberg neural networks with time-varying delays and reaction-diffusion terms , 2008, Neurocomputing.

[35]  Kunlun Wang,et al.  Dynamical behaviors of Cohen-Grossberg neural networks with delays and reaction-diffusion terms , 2006, Neurocomputing.

[36]  Huaguang Zhang,et al.  Robust stability criteria for interval Cohen-Grossberg neural networks with time varying delay , 2009, Neurocomputing.

[37]  Leon O. Chua,et al.  Fuzzy cellular neural networks: theory , 1996, 1996 Fourth IEEE International Workshop on Cellular Neural Networks and their Applications Proceedings (CNNA-96).

[38]  Jianlong Qiu,et al.  Exponential stability of impulsive neural networks with time-varying delays and reaction-diffusion terms , 2007, Neurocomputing.

[39]  Baotong Cui,et al.  Robust exponential stability of interval Cohen-Grossberg neural networks with time-varying delays , 2009 .

[40]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[41]  Daoyi Xu,et al.  Impulsive effects on stability of Cohen-Grossberg neural networks with variable delays , 2006, Appl. Math. Comput..

[42]  Weiwei Su,et al.  Global robust stability criteria of stochastic Cohen–Grossberg neural networks with discrete and distributed time-varying delays , 2009 .

[43]  Jinde Cao,et al.  Boundedness and stability for Cohen–Grossberg neural network with time-varying delays☆ , 2004 .

[44]  Yunong Zhang,et al.  New sufficient conditions for global asymptotic stability of Cohen–Grossberg neural networks with time-varying delays , 2009 .

[45]  Xiaofeng Liao,et al.  (Corr. to) Delay-dependent exponential stability analysis of delayed neural networks: an LMI approach , 2002, Neural Networks.

[46]  Linshan Wang,et al.  Global exponential robust stability of reaction¿diffusion interval neural networks with time-varying delays , 2006 .