This paper studies the problems of state bounding and $L_{\mathrm{\infty }}$-gain analysis for positive singular systems with unbounded time-variable delays and bounded disturbance for the first time. By a novel approach, we derive componentwise state bounds for positive singular system with or without bounded disturbances. An application to $L_{\mathrm{\infty }}$-gain problem of positive singular systems with unbounded time-variable delays is also presented. A numerical example is conducted to validate the effectiveness of our results.

中文翻译：

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具有无界时变延迟的正奇异系统的状态边界和 L∞-增益

本文研究了状态边界和 ${升}_{\mathrm{\infty }}$-首次对具有无界时变延迟和有界扰动的正奇异系统进行增益分析。通过一种新颖的方法，我们为有或没有有界干扰的正奇异系统推导了组件状态边界。申请${升}_{\mathrm{\infty }}$还提出了具有无界时变延迟的正奇异系统的增益问题。进行了一个数值例子来验证我们结果的有效性。