This note is concerned with the stability analysis of linear systems with a time-varying delay, where the delay is assumed to be a periodically varying bounded function with restricted derivatives. Combining the allowable delay set (ADS) definition and the region partitioning technique, an ADS partitioning approach is proposed, and then by with aid of this approach, a novel Lyapunov–Krasovskii functional (LKF), namely delay-set-partition-based (DSPB) LKF, is developed. Compared with the previous LKF method, the main advantage of the DSPB LKF lies in allowing the considered system to construct its own LKF in each sub-ADS. By utilizing the proposed LKF, less conservative stability criteria are derived. Finally, two simulation examples are provided to verify the effectiveness and superiority of the proposed method.

中文翻译：

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基于允许时滞集划分方法的线性时滞系统稳定性分析

本文涉及具有时变延迟的线性系统的稳定性分析，其中假设延迟是具有受限导数的周期性变化的有界函数。结合允许延迟集（ADS）定义和区域划分技术，提出了一种ADS划分方法，然后借助该方法，提出了一种新颖的Lyapunov-Krasovskii泛函（LKF），即基于延迟集划分的（ DSPB) LKF，已开发。与之前的LKF方法相比，DSPB LKF的主要优点在于允许所考虑的系统在每个子ADS中构造自己的LKF。通过利用所提出的 LKF，导出了不太保守的稳定性标准。最后提供两个仿真算例验证了所提方法的有效性和优越性。