This paper is concerned with the optimal H₂ filtering problem for continuous-time systems with multiplicative noise and multiple sampled delay measurements. The reorganized observation technique is firstly applied for treating the sampled delay terms, and then an equivalent delay-free sampled measurement is received. An optimal H₂ filter is constructed by using a dynamic model with finite jumps, which can provide the state estimation of the measurement sampling interval as well as the measurement sampling moments. The filter gain is given in terms of the stabilizing solution to a set of specific Riccati differential equations. It should be pointed out that no state augmentation is required, and thus the Riccati equation developed in this paper remain the same dimension as that of the original system state. This is the clear distinction from the state augmentation method. A practical example is finally supplied to illustrate the efficiency of the proposed results.

中文翻译：

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具有乘法噪声和采样数据的测量延迟系统的最佳 H2 过滤

本文关注具有乘性噪声和多次采样延迟测量的连续时间系统的最优H ₂滤波问题。首先应用重组观测技术处理采样延迟项，然后接收等效的无延迟采样测量。一个最优的H ₂滤波器是通过使用有限跳跃的动态模型构建的，它可以提供测量采样间隔以及测量采样时刻的状态估计。滤波器增益根据一组特定 Riccati 微分方程的稳定解给出。需要指出的是，不需要状态增广，因此本文提出的 Riccati 方程与原始系统状态保持相同的维数。这是与状态增强方法的明显区别。最后提供了一个实际例子来说明所提出结果的有效性。