This paper is concerned with the reachable set estimation (RSE) problem for singular systems with both time‐varying delays and bounded peak disturbances. The objective is to search a bounded set that contains all the system states under zero initial conditions. By utilizing the theory of {1}‐inverse and Wirtinger‐based integral inequality, an improved criterion is established in terms of the linear matrix inequalities (LMIs) to guarantee that the reachable set of time‐varying delay singular system is regular, impulse‐free and bounded by the intersection of ellipsoids. Here, a relaxed Lyapunov‐Krasovskii functional is employed to solve the addressed RSE problem which does not require all the involved symmetric matrices to be positive definite. Finally, numerical examples are provided to demonstrate the effectiveness of the proposed methods.

中文翻译：

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时变时滞奇异系统可达集估计的新结果

本文关注具有时变时滞和有界峰值干扰的奇异系统的可达集估计（RSE）问题。目的是搜索包含零初始条件下所有系统状态的有界集合。利用{1}的理论基于逆矩阵和基于Wirtinger的积分不等式，针对线性矩阵不等式（LMI）建立了改进的准则，以确保时变时滞奇异系统的可到达集合是规则的，无脉冲的并且受椭球的交集限制。在这里，使用松弛的Lyapunov-Krasovskii泛函来解决所解决的RSE问题，该问题不需要所有涉及的对称矩阵都是正定的。最后，通过数值算例证明了所提方法的有效性。