Some sufficient conditions for global exponential stability of delayed Hopfield neural networks

Authors:
Hongtao Lu;Fu-Lai Chung;Zhenya He
Affiliations:
Department of Computer Science and Engineering, Shanghai Jiao Tong University, Shanghai 200030, China;Center for Multimedia Signal Processing and Department of Computing, Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, China;Department of Radio Engineering, Southeast University, Nanjing 210096, Jiangsu Province, China
Venue:
Neural Networks
Year:
2004

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Abstract

In this paper, we have derived some sufficient conditions for existence and uniqueness of equilibrium and global exponential stability in delayed Hopfield neural networks by using a different approach from the usually used one where the existence, uniqueness of equilibrium and stability are proved in two separate steps, rather we first prove global exponential convergence to 0 of the difference between any two solutions of the original neural networks, the existence and uniqueness of equilibrium is the direct results of this procedure. We obtain the conditions by suitable construction of Lyapunov functionals and estimation of derivates of the Lyapunov functionals by the well-known Young's inequality and Holder's inequality. The proposed conditions are related to p-norms of vector or matrix, p ∈ [1, ∞], and thus unify and generalize some results in the literature.