Stability analysis for the generalized Cohen-Grossberg neural networks with inverse Lipschitz neuron activations

Authors:
Xiaobing Nie;Jinde Cao
Affiliations:
Department of Mathematics, Southeast University, Nanjing 210096, China;Department of Mathematics, Southeast University, Nanjing 210096, China
Venue:
Computers & Mathematics with Applications
Year:
2009

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Abstract

In this paper, by using nonsmooth analysis approach, linear matrix inequality (LMI) technique, topological degree theory and Lyapunov-Krasovskii function method, the issue of global exponential stability is investigated for a class of generalized Cohen-Grossberg neural networks possessing inverse Lipschitz neuron activations and nonsmooth behaved functions. Several novel delay-dependent sufficient conditions are established towards the existence, uniqueness and global exponential stability of the equilibrium point, which are shown in terms of LMIs. It is noted that the results above require neither the Lipschitz continuity of the activation functions, nor the smoothness of the behaved functions. Also, for the case of the activation function that satisfies not only the inverse Lipschitz conditions but also the Lipschitz conditions, some conditions are derived which generalize the previous results. Finally, two examples with their simulations are given to show the effectiveness of the theoretical results.