Robust exponential stability of interval Cohen-Grossberg neural networks with time-varying delays

Abstract In this paper, the problem of robust exponential stability for a class of interval Cohen–Grossberg neural networks with time-varying delays is investigated. Without assuming the boundedness and differentiability of the activation functions and any symmetry of interconnection matrices, some sufficient conditions for the existence, uniqueness, and global robust exponential stability of the equilibrium point are derived. Some comparisons between the results presented in this paper and the previous results admit that our results are the improvement and extension of the existed ones. The validity and performance of the new results are further illustrated by two simulation examples.

[1]  Wang,et al.  Qualitative analysis of Cohen-Grossberg neural networks with multiple delays. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[2]  Leon O. Chua,et al.  Neural networks for nonlinear programming , 1988 .

[3]  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).

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

[5]  Hongtao Lu.  Global exponential stability analysis of Cohen-Grossberg neural networks , 2005, IEEE Transactions on Circuits and Systems II: Express Briefs.

[6]  Kwok-Wo Wong,et al.  Robust stability of interval bidirectional associative memory neural network with time delays , 2004, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[7]  Jinde Cao,et al.  LMI-based criteria for global robust stability of bidirectional associative memory networks with time delay , 2007 .

[8]  Libin Rong.  LMI-based criteria for robust stability of Cohen–Grossberg neural networks with delay , 2005 .

[9]  Guanrong Chen,et al.  Novel robust stability criteria for interval-delayed Hopfield neural networks , 2001 .

[10]  Z. Guan,et al.  An LMI Approach to Exponential Stability Analysis of Neural Networks with Time-Varying Delay , 2005, TENCON 2005 - 2005 IEEE Region 10 Conference.

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

[12]  Y. Chen.  Global asymptotic stability of delayed Cohen-Grossberg neural networks , 2006, IEEE Transactions on Circuits and Systems I: Regular Papers.

[13]  Jin-Hua She,et al.  Delay-dependent exponential stability of delayed neural networks with time-varying delay , 2006, IEEE Transactions on Circuits and Systems II: Express Briefs.

[14]  Chuandong Li,et al.  Global Robust Stability Criteria for Interval Delayed Neural Networks Via an LMI Approach , 2006, IEEE Transactions on Circuits and Systems II: Express Briefs.

[15]  Stephen Grossberg,et al.  Absolute stability of global pattern formation and parallel memory storage by competitive neural networks , 1983, IEEE Transactions on Systems, Man, and Cybernetics.

[16]  Neyir Ozcan,et al.  Global robust stability analysis of neural networks with multiple time delays , 2006, IEEE Transactions on Circuits and Systems I: Regular Papers.

[17]  B. Cui,et al.  Global asymptotic stability of Cohen–Grossberg neural networks with constant and variable delays , 2007 .

[18]  B. Cui,et al.  Global robust exponential stability of delayed neural networks , 2008 .

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

[20]  M. Forti.  On Global Asymptotic Stability of a Class of Nonlinear Systems Arising in Neural Network Theory , 1994 .

[21]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[22]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[23]  A. Tesi,et al.  New conditions for global stability of neural networks with application to linear and quadratic programming problems , 1995 .

[24]  Jinde Cao,et al.  Robust Stability of Switched Cohen–Grossberg Neural Networks With Mixed Time-Varying Delays , 2006, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[25]  X. Zou,et al.  Harmless delays in Cohen–Grossberg neural networks ☆ , 2002 .

[26]  Sabri Arik,et al.  Global stability analysis of neural networks with multiple time varying delays , 2005, IEEE Transactions on Automatic Control.

[27]  Sabri Arik,et al.  An analysis of exponential stability of delayed neural networks with time varying delays , 2004, Neural Networks.

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

[29]  Xuyang Lou,et al.  On the global robust asymptotic stability of BAM neural networks with time-varying delays , 2006, Neurocomputing.

[30]  S. Arik,et al.  Global stability analysis of Cohen–Grossberg neural networks with time varying delays , 2005 .

[31]  Jinde Cao,et al.  Global asymptotic and robust stability of recurrent neural networks with time delays , 2005, IEEE Trans. Circuits Syst. I Regul. Pap..