This article presents an annular finite-time \(H_{\infty }\) filtering approach for continuous-time mean-field stochastic systems (MFSSs). Our attention is focused on obtaining a set of stability criteria for analyzing the \(H_{\infty }\) performance and the annular finite-time boundedness of the filtering error system. Sufficient conditions in the form of linear matrix inequality (LMI) are established to guarantee the existence of the designed filter. Then, the filter gains are derived through a convex optimization problem. Through a simulation example, the validity of the obtained results is demonstrated.

中文翻译：

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平均场随机系统的环形有限时间 $$H_{\infty }$$ 滤波

本文提出了一种适用于连续时间平均场随机系统 (MFSS) 的环形有限时间\(H_{\infty }\)滤波方法。我们的注意力集中在获得一组稳定性标准来分析过滤误差系统的\(H_{\infty }\)性能和环形有限时间有界性。建立了线性矩阵不等式（LMI）形式的充分条件来保证所设计的滤波器的存在性。然后，通过凸优化问题导出滤波器增益。通过仿真算例，验证了所得结果的有效性。