This paper studies the problem of reduced-order extended dissipative filters design for continuous-time singular Markovian jump systems with discrete and distributed delays. By proposing a new integral inequality, a sufficient condition based on linear matrix inequalities (LMIs) is presented to ensure the existence of the extended dissipative filters. Compared with the previous ones, the proposed method can sufficiently exploit the information on discrete and distributed delays. A set of slack matrices instead of fixed ones are introduced in the LMIs to find all solutions of the reduced-order filters, which can enhance the flexibility of the obtained result. Two numerical examples are provided to illustrate the effectiveness and advantages of the proposed filters design condition.

中文翻译：

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具有离散和分布式延迟的奇异马尔可夫跳跃系统的扩展耗散滤波器设计的一种新的积分不等式方法

本文研究了具有离散和分布式延迟的连续时间奇异马尔可夫跳跃系统的降阶扩展耗散滤波器设计问题。通过提出一个新的积分不等式，提出了一个基于线性矩阵不等式（LMI）的充分条件来保证扩展耗散滤波器的存在。与以前的方法相比，所提出的方法可以充分利用离散和分布式延迟的信息。在 LMI 中引入一组松弛矩阵而不是固定矩阵来寻找降阶滤波器的所有解，这可以增强所获得结果的灵活性。提供了两个数值例子来说明所提出的滤波器设计条件的有效性和优点。