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**Global exponential stability of impulsive discrete-time neural networks with time-varying delays.**
*(English)*
Zbl 1207.93086

Summary: This paper studies the problem of global exponential stability and exponential convergence rate for a class of impulsive discrete-time neural networks with time-varying delays. Firstly, by means of Lyapunov’s stability theory, some inequality analysis techniques and a discrete-time Halanay-type inequality technique, sufficient conditions for ensuring global exponential stability of discrete-time neural networks are derived, and the estimated exponential convergence rate is provided as well. The obtained results are then applied to derive global exponential stability criteria and exponential convergence rate of impulsive discrete-time neural networks with time-varying delays. Finally, numerical examples are provided to illustrate the effectiveness and usefulness of the obtained criteria.

### MSC:

93D20 | Asymptotic stability in control theory |

93C55 | Discrete-time control/observation systems |

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

### Keywords:

impulsive discrete-time neural networks; global exponential stability; exponential convergence rate; Halanay inequality
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\textit{H. Xu} et al., Appl. Math. Comput. 217, No. 2, 537--544 (2010; Zbl 1207.93086)

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