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**LMI criteria on exponential stability of BAM neural networks with both time-varying delays and general activation functions.**
*(English)*
Zbl 1204.92006

Summary: Exponential stability analysis for a bidirectional associative memory neural network model with both time-varying delays and general activation functions is considered. Neither the boundedness and the monotony on these activation functions nor the differentiability on the time-varying delays are assumed. By employing Lyapunov functionals and a linear matrix inequality (LMI) approach, several new sufficient conditions in LMI form are obtained to ensure the existence, uniqueness and global exponential stability of equilibrium points for the neural network. Moreover, the exponential convergence rate index is estimated, which depends on the system parameters. The proposed stability results are less conservative than some recently known ones in the literature, which is demonstrated via an example with simulation.

### MSC:

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

68T05 | Learning and adaptive systems in artificial intelligence |

15A39 | Linear inequalities of matrices |

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

37N25 | Dynamical systems in biology |

34K20 | Stability theory of functional-differential equations |

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\textit{H. Wang} et al., Math. Comput. Simul. 81, No. 4, 837--850 (2010; Zbl 1204.92006)

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### References:

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