In this article, the problem of unified filters design including H_∞, L₂ − L_∞, passive, dissipative filters and their reduced‐order ones is addressed for continuous‐time singular Markovian jump systems with discrete and distributed delays. Unlike some existing works, the mixed delays can be fully captured by proposing an extended free‐matrix‐based integral inequality. By considering two cases of distributed delays, two novel criteria are presented to ensure the filtering error system to be stochastically admissible and extended dissipative. Some numerical examples are provided to illustrate the effectiveness of the unified filter design methods.

中文翻译：

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基于扩展的基于自由矩阵的不等式方法的混合时滞奇异马尔可夫跳跃系统的统一滤波器

在这篇文章中，统一滤波器的设计问题包括ħ _∞，大号₂  - 大号_∞，被动的，耗散过滤器及其降阶那些用于与离散分布时滞连续时间马尔可夫奇异跳跃系统被寻址。与某些现有作品不同，可以通过提出扩展的基于自由矩阵的积分不等式来完全捕获混合延迟。通过考虑分布延迟的两种情况，提出了两种新颖的标准，以确保滤波误差系统是随机允许的并且具有耗散的扩展性。提供了一些数值示例来说明统一滤波器设计方法的有效性。