In this paper, we study the problem of estimating states and faults for a class of linear time-delay systems using sliding mode observers. Both the states and outputs are subject to constant delays. This is a challenging problem and has not yet been resolved in the literature. By appropriately using a system transformation and the ${\mathcal{H}}_{\infty }$ filtering method, we propose a novel sliding mode observer scheme which can guarantee ${\mathcal{H}}_{\infty }$ asymptotic stability of the state and fault estimation errors. A numerical example is provided to illustrate the effectiveness of the new result.

中文翻译：

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滑模观测器，用于估计线性时滞系统的状态和故障，其输出会受到延迟的影响

在本文中，我们研究使用滑模观测器估计一类线性时滞系统的状态和故障的问题。状态和输出都受到恒定的延迟。这是一个具有挑战性的问题，尚未在文献中得到解决。通过适当地使用系统转换和${\mathcal{H}}_{\infty }$ 滤波方法，我们提出了一种新颖的滑模观测器方案，可以保证 ${\mathcal{H}}_{\infty }$状态的渐近稳定性和故障估计误差。提供了一个数值示例来说明新结果的有效性。