This paper is concerned with the stability of the linear systems with a time-varying delay. First, we derive a new form of constrained quadratic matrix inequality for the reciprocally convex inequality. Second, an equivalent transform of a constrained quadratic matrix inequality into the form of a linear matrix inequality(LMI) is derived. Third, the upper bound of the time derivative of Lyapunov Krasovskii functional(LKF), in the form of a constrained quadratic matrix, is obtained, and an equivalent transform is done to make it in the form of LMI. Finally, the improvement in stability is shown through two well-known examples.

中文翻译：

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通过新的约束二次矩阵不等式提高时滞线性系统的稳定性

本文关注具有时变延迟的线性系统的稳定性。首先，我们为互凸不等式推导出一种新形式的约束二次矩阵不等式。其次，导出了约束二次矩阵不等式到线性矩阵不等式(LMI)形式的等效变换。第三，得到Lyapunov Krasovskii泛函(LKF)的时间导数的上界，以约束二次矩阵的形式，并进行等效变换，使其成为LMI的形式。最后，通过两个众所周知的例子展示了稳定性的提高。