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**Switched exponential state estimation and robust stability for interval neural networks with discrete and distributed time delays.**
*(English)*
Zbl 1246.93088

Summary: The interval exponential state estimation and robust exponential stability for the switched interval neural networks with discrete and distributed time delays are considered. Firstly, by combining the theories of the switched systems and the interval neural networks, the mathematical model of the switched interval neural networks with discrete and distributed time delays and the interval estimation error system are established. Secondly, by applying the augmented Lyapunov-Krasovskii functional approach and available output measurements, the dynamics of estimation error system is proved to be globally exponentially stable for all admissible time delays. Both the existence conditions and the explicit characterization of desired estimator are derived in terms of linear matrix inequalities (LMIs). Moreover, a delay-dependent criterion is also developed, which guarantees the robust exponential stability of the switched interval neural networks with discrete and distributed time delays. Finally, two numerical examples are provided to illustrate the validity of the theoretical results.

### MSC:

93D09 | Robust stability |

93E10 | Estimation and detection in stochastic control theory |

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

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\textit{H. Xu} et al., Abstr. Appl. Anal. 2012, Article ID 103542, 20 p. (2012; Zbl 1246.93088)

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