Synchronization of recurrent neural networks with mixed time-delays via output coupling with delayed feedback.

*(English)*Zbl 1267.93138Summary: This paper deals with the synchronization control problem for the recurrent neural networks with discrete and distributed delays. By introducing an improved Lyapunov-Krasovskii functional and employing convex combination approach, a delay-dependent output feedback controller is derived to achieve synchronization with the help of a master-slave concept and linear matrix inequality approach. Moreover, the activation functions are assumed to be of more general descriptions, which generalize and improve many of those existing methods. It is worth noting that the traditional assumptions on the differentiability of the time-varying delays and the boundedness of its derivative are removed explicitly. Finally, numerical results and its simulations are given to show the effectiveness of the derived results.

##### MSC:

93D15 | Stabilization of systems by feedback |

93C15 | Control/observation systems governed by ordinary differential equations |

34D06 | Synchronization of solutions to ordinary differential equations |

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

34K25 | Asymptotic theory of functional-differential equations |

##### Keywords:

neural networks; synchronization; time delays; Lyapunov-krasovskii functional; linear matrix inequalities
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\textit{P. Balasubramaniam} and \textit{V. Vembarasan}, Nonlinear Dyn. 70, No. 1, 677--691 (2012; Zbl 1267.93138)

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