Global exponential stability of a class of neural circuits

This paper obtains the global exponential stability (GES) of the class of Hopfield-Tank neural circuits, which can represent a generalization of the existing stability results in the sense that only the global asymptotic stability (GAS) of the neural circuits was obtained under existing sufficient conditions in the literature. An example of a neural circuit which is globally asymptotically stable (GAS) rather than globally exponentially stable (GES) is also given.

[1]  C. A. Desoer,et al.  Nonlinear Systems Analysis , 1978 .

[2]  J J Hopfield,et al.  Neurons with graded response have collective computational properties like those of two-state neurons. , 1984, Proceedings of the National Academy of Sciences of the United States of America.

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

[4]  T. Roska.  Some qualitative aspects of neural computing circuits , 1988, 1988., IEEE International Symposium on Circuits and Systems.

[5]  Morris W. Hirsch,et al.  Convergent activation dynamics in continuous time networks , 1989, Neural Networks.

[6]  D. Kelly,et al.  Stability in contractive nonlinear neural networks , 1990, IEEE Transactions on Biomedical Engineering.

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

[8]  Mauro Forti,et al.  On a class of nonsymmetrical neural networks with application to ADC , 1991 .

[9]  M. Forti,et al.  A condition for global convergence of a class of symmetric neural circuits , 1992 .

[10]  Kiyotoshi Matsuoka,et al.  Stability conditions for nonlinear continuous neural networks with asymmetric connection weights , 1992, Neural Networks.

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

[14]  M. Forti,et al.  Necessary and sufficient condition for absolute stability of neural networks , 1994 .

[15]  Tharam S. Dillon,et al.  Exponential stability and oscillation of Hopfield graded response neural network , 1994, IEEE Trans. Neural Networks.

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

[17]  Eugenius Kaszkurewicz,et al.  Comments on "Necessary and sufficient condition for absolute stability of neural networks" , 1995 .