Abstract This paper investigates the H∞ performance state estimation problem for static neural networks with time-varying delays. A parameter-dependent reciprocally convex inequality (PDRCI) is presented, which encompasses some existing results as its special cases. By dividing the estimation error of activation function into two parts, an improved Lyapunov-Krasovskii functional (LKF) is constructed, in which the slope information of activation function (SIAF) can be fully captured. Combining PDRCI and the improved LKF, a new criterion is obtained to ensure the estimation error system to be asymptotically stable with H∞ performance. By using a decoupling principle, the estimator gain matrices are solved in terms of linear matrix inequalities (LMIs). Compared with some existing works, the restrictions on slack matrices are overcome, which directly leads to performance improvement and reduction of conservativeness in the estimator solution. Two examples are illustrated to verify the advantages of the developed criterion.

中文翻译：

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时变时滞静态神经网络H∞性能状态估计的新结果

摘要 本文研究了具有时变延迟的静态神经网络的 H∞ 性能状态估计问题。提出了一个依赖于参数的互反凸不等式（PDRCI），它包含一些现有结果作为其特例。通过将激活函数的估计误差分为两部分，构建了一个改进的Lyapunov-Krasovskii函数（LKF），其中可以充分捕捉激活函数（SIAF）的斜率信息。结合 PDRCI 和改进的 LKF，获得了一个新的准则，以确保估计误差系统在 H∞ 性能下渐近稳定。通过使用去耦原理，估计器增益矩阵根据线性矩阵不等式 (LMI) 求解。与现有的一些作品相比，克服了松弛矩阵的限制，这直接导致了估计器解决方案中的性能改进和保守性的减少。举例说明了两个例子来验证所开发的标准的优点。