An LMI approach to global asymptotic stability of the delayed Cohen-Grossberg neural network via nonsmooth analysis

Authors:
Wenwu Yu;Jinde Cao;Jun Wang
Affiliations:
Department of Mathematics, Southeast University, Nanjing 210096, Jiangsu, China and Department of Electrical Engineering, Columbia University, New York, NY 10027, USA;Department of Mathematics, Southeast University, Nanjing 210096, Jiangsu, China;Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong
Venue:
Neural Networks
Year:
2007

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Abstract

In this paper, a linear matrix inequality (LMI) to global asymptotic stability of the delayed Cohen-Grossberg neural network is investigated by means of nonsmooth analysis. Several new sufficient conditions are presented to ascertain the uniqueness of the equilibrium point and the global asymptotic stability of the neural network. It is noted that the results herein require neither the smoothness of the behaved function, or the activation function nor the boundedness of the activation function. In addition, from theoretical analysis, it is found that the condition for ensuring the global asymptotic stability of the neural network also implies the uniqueness of equilibrium. The obtained results improve many earlier ones and are easy to apply. Some simulation results are shown to substantiate the theoretical results.