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**LMI conditions for stability of neural networks with distributed delays.**
*(English)*
Zbl 1146.34331

This paper presents new sufficient conditions for global asymptotic stability of neural networks with discrete and distributed delays. By using appropriate Lyapunov-Krasovskii functionals, authors derive stability conditions in terms of linear matrix inequalities (LMIs). This is convenient for numerical checking the stability of the network using the powerful MATLAB LMI Toolbox. Moreover, existing conditions are mostly based on certain diagonal dominance or \(M\) matrix conditions on weight matrices of the neural networks, which only make use of absolute values of the weights and ignore their sign, and hence are somewhat conservative. The LMI-based results obtained here can get rid of this disadvantage and give less conservative stability conditions. The authors illustrate this with numerical examples.

Reviewer: A. A. Martynyuk (Kyïv)

### MSC:

34K20 | Stability theory of functional-differential equations |

37N25 | Dynamical systems in biology |

92B20 | Neural networks for/in biological studies, artificial life and related topics |

### Keywords:

neural networks; Lyapunov–Krasovsky functional; linear matrix inequalities; stability conditions
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\textit{H. Yang} and \textit{T. Chu}, Chaos Solitons Fractals 34, No. 2, 557--563 (2007; Zbl 1146.34331)

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