This paper mainly investigates the admissibility analysis and the admissibilizing controller design for the uncertain discrete singular system with delayed state. Based on Lyapunov–Krasovskii stability theory, an original admissibility condition for the nominal singular delay system is first presented. By involving the uncertainties in both difference and system matrices simultaneously, we devote to analyzing the robust admissibility for the regarded uncertain discrete singular system with delayed state. Furthermore, by hiring the state feedback control law, we further discuss the admissibilizing controller design for the resulting closed-loop system. Since all the derived criteria are expressed in terms of strict linear matrix inequalities (LMIs) or parametric LMIs, we thus can handily verify them via current LMI solvers. Finally, two numerical examples are given to illustrate the effectiveness and validity of the proposed approach.

中文翻译：

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包含差异和系统矩阵不确定性的离散奇异时滞系统的可容许性分析和控制器设计

本文主要研究时滞不确定离散广义系统的可容许性分析和可容许性控制器的设计。基于Lyapunov–Krasovskii稳定性理论，首次提出了标称奇异时滞系统的原始容许条件。通过同时考虑差分和系统矩阵中的不确定性，我们致力于分析被认为具有时滞状态的不确定离散奇异系统的鲁棒可容许性。此外，通过采用状态反馈控制律，我们进一步讨论了所得闭环系统的可容许控制器设计。由于所有导出的标准均以严格的线性矩阵不等式（LMI）或参数LMI表示，因此我们可以通过当前的LMI求解器方便地验证它们。最后，