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**Delay-dependent exponential stability for impulsive Cohen-Grossberg neural networks with time-varying delays and reaction-diffusion terms.**
*(English)*
Zbl 1221.35440

Summary: A class of impulsive Cohen-Grossberg neural networks with time-varying delays and reaction-diffusion is formulated and investigated. By employing delay differential inequality and the linear matrix inequality (LMI) optimization approach, some sufficient conditions ensuring global exponential stability of equilibrium point for impulsive Cohen-Grossberg neural networks with time-varying delays and diffusion are obtained. In particular, the estimate of the exponential convergence rate is also provided, which depends on system parameters, diffusion effect and impulsive disturbed intention. It is believed that these results are significant and useful for the design and applications of Cohen-Grossberg neural networks. An example is given to show the effectiveness of the results obtained here.

### MSC:

35R12 | Impulsive partial differential equations |

35B35 | Stability in context of PDEs |

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

### Keywords:

Cohen-Grossberg neural networks; impulses; delays; global exponential stability; linear matrix inequality
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\textit{X. Zhang} et al., Commun. Nonlinear Sci. Numer. Simul. 16, No. 3, 1524--1532 (2011; Zbl 1221.35440)

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