The Lyapunov-Krasovskii functional (LKF) method is an effective tool to obtain delay-dependent stability criteria of time-varying delay systems. However, in the method, the requirement that there must exist an appropriate LKF for a system with a delay varying in a delay interval is too strict and may lead to considerable conservativeness. In order to get less conservative stability criteria, a novel stability analysis method called a delay-mode-based LKF (DMBLKF) method is first presented for nonlinear delay systems. Compared with the LKF method, the main advantage of the DMBLKF method lies in relaxing the aforementioned requirement and leading to a less conservative criterion in stability analysis. Then, with the help of the novel method, new stability criteria of linear delay systems are derived. Finally, the effectiveness of the proposed method and the obtained criteria is illustrated through two numerical examples.

中文翻译：

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时变时滞系统稳定性分析新方法


Lyapunov-Krasovskii 泛函 (LKF) 方法是获得时变时滞系统的时滞相关稳定性准则的有效工具。然而，该方法对于时延间隔变化的系统必须存在合适的LKF的要求过于严格，可能导致相当保守。为了获得不太保守的稳定性准则，首先针对非线性时滞系统提出了一种新的稳定性分析方法，称为基于时滞模式的LKF（DMBLKF）方法。与LKF方法相比，DMBLKF方法的主要优点在于放宽了上述要求并导致稳定性分析中保守性较低的标准。然后，借助新方法，推导了线性时滞系统的新稳定性判据。最后，通过两个数值例子说明了所提出方法和所获得准则的有效性。