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**Global robust stability for stochastic interval neural networks with continuously distributed delays of neutral type.**
*(English)*
Zbl 1196.34107

Consider stochastic interval neural networks with distributed delays of neutral type equation:

\[ \begin{split} d[x(t) - Dx(t-\mu (t))] =\\ \bigg [ -Ax(t) +W^{(1)}f(x(t)) + W^{(2)}f(x(t-\tau(t)))+ W^{(3)}\int_{-\infty}^t K(t-s)f(x(s))ds \bigg ] dt \\+ \sigma(t,x(t),x(t-\tau(t)), x(t-\mu(t)))d\omega(t).\end{split} \]

The author studies stochastic stability for interval neural networks with continuously distributed delays of neutral type. Using a Lyapunov-Krasovskii functional and LMI technique, the author obtains sufficient conditions for global robust stability. Obtained results are demonstrated by using the MATLAB LMI control toolbox.

\[ \begin{split} d[x(t) - Dx(t-\mu (t))] =\\ \bigg [ -Ax(t) +W^{(1)}f(x(t)) + W^{(2)}f(x(t-\tau(t)))+ W^{(3)}\int_{-\infty}^t K(t-s)f(x(s))ds \bigg ] dt \\+ \sigma(t,x(t),x(t-\tau(t)), x(t-\mu(t)))d\omega(t).\end{split} \]

The author studies stochastic stability for interval neural networks with continuously distributed delays of neutral type. Using a Lyapunov-Krasovskii functional and LMI technique, the author obtains sufficient conditions for global robust stability. Obtained results are demonstrated by using the MATLAB LMI control toolbox.

Reviewer: Haydar Akca (Al Ain)

### MSC:

34K50 | Stochastic functional-differential equations |

34K20 | Stability theory of functional-differential equations |

34K40 | Neutral functional-differential equations |

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

### Keywords:

stochastic interval neural networks; global robust stability; Lyapunov-Krasovskii functional; linear matrix inequality (LMI); continuously distributed delays### Software:

Matlab
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\textit{X. Li}, Appl. Math. Comput. 215, No. 12, 4370--4384 (2010; Zbl 1196.34107)

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