In this paper, the problem of linear functional state bounding for linear positive singular system with an interval time‐varying delay is investigated for the first time. First, the authors present new conditions for positivity, regularity, impulse free, and the existence of componentwise bound for the state vector of the singular systems without disturbance. Based on the obtained results, and by using state transformations, we derive the smallest componentwise ultimate bound of the state vector of the linear positive singular system with bounded disturbances. Then, we propose some sufficient criteria for linear functional state bounding problems of the positive singular system with time‐varying delays by using some new mathematical techniques. Since the conditions are given in terms of the linear programming/Hurwit matrix/spectral abscissa, we can check them easily and compute directly the smallest componentwise ultimate bound. Finally, a numerical example is given to demonstrate the correctness and the effectiveness of the proposed methodology.

中文翻译：

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线性正奇异系统的线性功能状态有界，扰动在有界集内变化。

本文首次研究了具有时变时滞的线性正奇异系统的线性功能状态界问题。首先，作者提出了关于正性，规则性，无脉冲性以及奇异系统状态向量无扰动存在分量约束的新条件。基于获得的结果，并通过使用状态变换，我们推导了带有界扰动的线性正奇异系统的状态向量的最小分量最终极限。然后，通过使用一些新的数学技术，我们为时变时滞正奇异系统的线性功能状态边界问题提出了一些充分的判据。由于条件是根据线性规划/ Hurwit矩阵/光谱横坐标给出的，我们可以轻松地检查它们，并直接计算最小的组件最终极限。最后，通过数值例子说明了所提方法的正确性和有效性。