Global Robust Exponential Stability of Interval Neural Networks with Delays

In this Letter, based on globally Lipschitz continous activation functions, new conditions ensuring existence, uniqueness and global robust exponential stability of the equilibrium point of interval neural networks with delays are obtained. The delayed Hopfield network, Bidirectional associative memory network and Cellular neural network are special cases of the network model considered in this Letter.

[1]  John J. Hopfield,et al.  Simple 'neural' optimization networks: An A/D converter, signal decision circuit, and a linear programming circuit , 1986 .

[2]  Xue-Bin Liang,et al.  Global exponential stability of neural networks with globally Lipschitz continuous activations and its application to linear variational inequality problem , 2001, IEEE Trans. Neural Networks.

[3]  Xue-Zhong He,et al.  Delay-independent stability in bidirectional associative memory networks , 1994, IEEE Trans. Neural Networks.

[4]  S. Arik,et al.  On the global asymptotic stability of delayed cellular neural networks , 2000 .

[5]  Changyin Sun,et al.  On exponential stability of delayed neural networks with globally Lipschitz continuous activation functions , 2002, Proceedings of the 4th World Congress on Intelligent Control and Automation (Cat. No.02EX527).

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

[7]  Slawomir Kuklinski,et al.  Cellular neural network application to moire pattern filtering , 1990, IEEE International Workshop on Cellular Neural Networks and their Applications.

[8]  Masahiko Morita,et al.  Associative memory with nonmonotone dynamics , 1993, Neural Networks.

[9]  Tianping Chen Convergence of Delayed Dynamical Systems , 2004, Neural Processing Letters.

[10]  Lin-Bao Yang,et al.  Cellular neural networks: theory , 1988 .

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

[12]  E. Kaszkurewicz,et al.  On a class of globally stable neural circuits , 1994 .

[13]  Leon O. Chua,et al.  Cellular neural networks: applications , 1988 .

[14]  L. Pandolfi,et al.  On stability of cellular neural networks with delay , 1993 .

[15]  Pauline van den Driessche,et al.  Global Attractivity in Delayed Hopfield Neural Network Models , 1998, SIAM J. Appl. Math..

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

[17]  Mathukumalli Vidyasagar,et al.  Location and stability of the high-gain equilibria of nonlinear neural networks , 1993, IEEE Trans. Neural Networks.

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

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

[20]  J. Hopfield Neurons withgraded response havecollective computational properties likethoseoftwo-state neurons , 1984 .

[21]  Jinde Cao,et al.  ABSOLUTE EXPONENTIAL STABILITY OF A CLASS OF NEURAL NETWORKS , 2002 .

[22]  J. Hale Theory of Functional Differential Equations , 1977 .

[23]  K. Gopalsamy,et al.  Stability in asymmetric Hopfield nets with transmission delays , 1994 .

[24]  Xiaofeng Liao,et al.  Robust stability for interval Hopfield neural networks with time delay , 1998, IEEE Trans. Neural Networks.

[25]  Masahiko Morita,et al.  Capacity of associative memory using a nonmonotonic neuron model , 1993, Neural Networks.

[26]  Jinde Cao,et al.  Stability analysis of delayed cellular neural networks , 1998, Neural Networks.

[27]  Tamcis Roska Analogic computing: system aspects of analogic CNN sensor computers , 2000, Proceedings of the 2000 6th IEEE International Workshop on Cellular Neural Networks and their Applications (CNNA 2000) (Cat. No.00TH8509).