This paper studies the stability problems of linear systems with time-varying delays. Firstly, an extended reciprocally convex quadratic inequality and an improved quadratic function negative-determination condition are proposed. Based on the method proposed, some less conservative criteria are derived. Finally, a well-known numerical example is carried out to demonstrate the effectiveness and the merits of the proposed method.

中文翻译：

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时滞时滞系统通过扩展的倒数二次凸不等式的层级稳定性条件

本文研究时变时滞线性系统的稳定性问题。首先，提出了扩展的倒凸二次不等式和改进的二次函数负确定条件。基于提出的方法，得出了一些不太保守的标准。最后，通过一个著名的数值例子来证明所提方法的有效性和优点。