On exponential stability analysis for neural networks with time-varying delays and general activation functions.

*(English)*Zbl 1239.92005Summary: This paper is concerned with the exponential stability analysis for a class of cellular neural networks with both interval time-varying delays and general activation functions. The boundedness assumption of the activation function is not required. The limitation on the derivative of the time delay being less than one is relaxed and the lower bound of time-varying delay is not restricted to be zero. A new Lyapunov-Krasovskii functional involving more information on the state variables is established to derive a novel exponential stability criterion. The obtained condition shows potential advantages over the existing ones since no useful item is ignored throughout the estimate of upper bound of the derivative of the Lyapunov functional. Finally, three numerical examples are included to illustrate the proposed design procedures and applications.

##### MSC:

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

34K20 | Stability theory of functional-differential equations |

65C20 | Probabilistic models, generic numerical methods in probability and statistics |

68T05 | Learning and adaptive systems in artificial intelligence |

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\textit{Y. Wang} et al., Commun. Nonlinear Sci. Numer. Simul. 17, No. 3, 1447--1459 (2012; Zbl 1239.92005)

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