Stability and dissipativity analysis of static neural networks with interval time-varying delay.

*(English)*Zbl 1307.93446Summary: This paper focuses on the problems of stability and dissipativity analysis for static Neural Networks (NNs) with interval time-varying delay. A new augmented Lyapunov-Krasovskii functional is firstly constructed, in which the information on the activation function is taken fully into account. Then, by employing a Wirtinger-based inequality to estimate the derivative of Lyapunov-Krasovskii functional, an improved stability criterion is derived for the considered neural networks. The result is extended to dissipativity analysis and a sufficient condition is established to assure the neural networks strictly dissipative. Two numerical examples are provided to demonstrate the effectiveness and the advantages of the proposed method.

##### MSC:

93E15 | Stochastic stability in control theory |

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

93D30 | Lyapunov and storage functions |

##### Keywords:

stability; dissipativity analysis; static neural networks (NNs); Lyapunov-Krasovskii functional; Wirtinger-based inequality
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\textit{H.-B. Zeng} et al., J. Franklin Inst. 352, No. 3, 1284--1295 (2015; Zbl 1307.93446)

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