In the estimation problem for delayed static neural networks (SNNs), constructing a proper Lyapunov-Krasovskii functional (LKF) is crucial for deriving less conservative estimation criteria. In this paper, a delay-product-type LKF with negative definite terms is proposed. Based on the third-order Bessel-Legendre (B-L) integral inequality and mixed convex combination approaches, a less conservative estimator design criterion is derived. Furthermore, the desired estimator gain matrices and the H∞ performance index are obtained by solving a set of linear matrix inequalities (LMIs). Finally, a numerical example is given to demonstrate the effectiveness of the proposed method.

中文翻译：

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通过带有负定项的Lyapunov-Krasovskii泛函的延迟静态神经网络的新H∞状态估计准则。

在延迟静态神经网络（SNN）的估计问题中，构造适当的Lyapunov-Krasovskii泛函（LKF）对于得出较不保守的估计标准至关重要。本文提出了具有负定项的时滞积型LKF。基于三阶Bessel-Legendre（BL）积分不等式和混合凸组合方法，得出了一个较不保守的估计器设计准则。此外，通过求解一组线性矩阵不等式（LMI），可以获得所需的估计器增益矩阵和H∞性能指标。最后，通过数值例子说明了该方法的有效性。