This paper studies the stability problem of time-varying delay systems. Firstly, By constructing a delay-product Lyapunov-Krasovskii functional, a stability criterion is established, where the advantages of convexity properties are being exploited. This stability criterion in terms of linear matrix inequality (LMI) can be checked exactly using an improved negativity condition of quadratic polynomials. It is demonstrated in the numeric examples that the proposed method can greatly reduce the conservativeness without leading to increase the number of decision variables.

中文翻译：

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时变时滞系统的层级稳定性条件

本文研究时变时滞系统的稳定性问题。首先，通过构造时滞积Lyapunov-Krasovskii泛函，建立了一个稳定性判据，利用了凸性质的优势。使用改进的二次多项式的负性条件，可以精确地检查基于线性矩阵不等式（LMI）的稳定性标准。数值算例表明，该方法在不增加决策变量数量的情况下，可以大大降低算法的保守性。