GLOBAL EXPONENTIAL STABILITY FOR REACTION-DIFFUSION RECURRENT NEURAL NETWORKS WITH MULTIPLE TIME-VARYING DELAYS

488 ABSTRACT In this paper, we consider the problem of exponential stability for recurrent neural networks with multiple time-varying delays and reaction–diffusion terms. The activation functions are supposed to be bounded and globally Lipschitz continuous. By means of Lyapunov functionals, sufficient conditions are derived, which guarantee global exponential stability of the delayed neural network. Finally, a numerical example is given to show the correctness of our analysis.

[1]  Jinde Cao,et al.  Absolute exponential stability of recurrent neural networks with Lipschitz-continuous activation functions and time delays , 2004, Neural Networks.

[2]  S. Arik.  Stability analysis of delayed neural networks , 2000 .

[3]  Xiaofeng Liao,et al.  Global robust asymptotical stability of multi-delayed interval neural networks: an LMI approach , 2004 .

[4]  J. Lam,et al.  Novel global robust stability criteria for interval neural networks with multiple time-varying delays , 2005 .

[5]  Xuyang Lou,et al.  Absolute exponential stability analysis of delayed bi-directional associative memory neural networks , 2007 .

[6]  Malur K. Sundareshan,et al.  Exponential stability and a systematic synthesis of a neural network for quadratic minimization , 1991, Neural Networks.

[7]  Lin Wang,et al.  Exponential stability of Cohen-Grossberg neural networks , 2002, Neural Networks.

[8]  Xuyang Lou,et al.  Boundedness and exponential stability for nonautonomous RCNNs with distributed delays , 2007, Comput. Math. Appl..

[9]  Zhaohui Yuan,et al.  Global stability analysis of a class of delayed cellular neural networks , 2005, Math. Comput. Simul..

[10]  Hongtao Lu,et al.  On stability of nonlinear continuous-time neural networks with delays , 2000, Neural Networks.

[11]  Shu-Cherng Fang,et al.  Neurocomputing with time delay analysis for solving convex quadratic programming problems , 2000, IEEE Trans. Neural Networks Learn. Syst..

[12]  Zhidong Teng,et al.  A new criterion on the global exponential stability for cellular neural networks with multiple time-varying delays , 2005 .

[13]  Jinde Cao,et al.  Delay-independent exponential stability of stochastic Cohen–Grossberg neural networks with time-varying delays and reaction–diffusion terms , 2007 .

[14]  Xuyang Lou,et al.  Stochastic Exponential Stability for Markovian Jumping BAM Neural Networks With Time-Varying Delays , 2007, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[15]  Jinde Cao,et al.  Global Asymptotical Stability of Recurrent Neural Networks With Multiple Discrete Delays and Distributed Delays , 2006, IEEE Transactions on Neural Networks.

[16]  Jinde Cao,et al.  Global exponential stability of reaction–diffusion recurrent neural networks with time-varying delays , 2003 .

[17]  Xuyang Lou,et al.  New LMI conditions for delay-dependent asymptotic stability of delayed Hopfield neural networks , 2006, Neurocomputing.

[18]  Abdesselam Bouzerdoum,et al.  Neural network for quadratic optimization with bound constraints , 1993, IEEE Trans. Neural Networks.

[19]  Jinde Cao,et al.  Exponential Stability for Impulsive BAM Neural Networks with Time-Varying Delays and Reaction-Diffusion Terms , 2007 .

[20]  Qiang Zhang,et al.  Stability of cellular neural networks with delay , 2001 .

[21]  Q. Song,et al.  Global exponential stability of BAM neural networks with distributed delays and reaction–diffusion terms , 2005 .

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

[23]  Wei Jing.  Stability of cellular neural networks with delay , 2007 .

[24]  X. Lou,et al.  Global asymptotic stability of BAM neural networks with distributed delays and reaction–diffusion terms , 2006 .

[25]  Angela Slavova,et al.  Stability analysis of cellular neural networks with nonlinear dynamics , 2001 .

[26]  Changyin Sun,et al.  Exponential periodicity and stability of delayed neural networks , 2004, Math. Comput. Simul..

[27]  Chuandong Li,et al.  An LMI approach to asymptotical stability of multi-delayed neural networks , 2005 .