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A general framework for global asymptotic stability analysis of delayed neural networks based on LMI approach. (English) Zbl 1072.92004

Summary: Global asymptotic stability is discussed for neural networks with time-varying delay. Several new criteria in matrix inequality form are given to ascertain the uniqueness and global asymptotic stability of equilibrium points for neural networks with time-varying delay based on Lyapunov method and Linear Matrix Inequality (LMI) techniques. The proposed LMI approach has the advantage of considering the difference of neuronal excitatory and inhibitory efforts, which is also computationally efficient as it can be solved numerically using a recently developed interior-point algorithm. In addition, the proposed results generalize and improve previous works. The obtained criteria also combine two existing conditions into one generalized condition in matrix form. An illustrative example is also given to demonstrate the effectiveness of the proposed results.

MSC:

92B20 Neural networks for/in biological studies, artificial life and related topics
34K20 Stability theory of functional-differential equations
15A45 Miscellaneous inequalities involving matrices
68T05 Learning and adaptive systems in artificial intelligence
34K60 Qualitative investigation and simulation of models involving functional-differential equations
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