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Some sufficient conditions for global exponential stability of delayed Hopfield neural networks. (English) Zbl 1091.68094

Summary: 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 Hölder’s inequality. The proposed conditions are related to \(p\)-norms of vector or matrix, \(p\in[1,\infty]\), and thus unify and generalize some results in the literature.

MSC:

68T05 Learning and adaptive systems in artificial intelligence
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
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