The aim of this article is to investigate the stability of sampled-data systems (SDSs) by introducing a sawtooth-characteristic-based hierarchical integral inequality (SCBHII) and to obtain the maximum allowable sampling period that maintains the stability of the system. First, by associating the sawtooth characteristics of the input delay in SDSs with free matrices, an SCBHII is proposed; its accuracy improves as the hierarchy increases. Subsequently, a high-order two-sided looped-functional, which considers both the sampling multi-integral states and the sawtooth pattern, is introduced to cater to the aforementioned inequality. In addition, the system variables are augmented by sawtooth pattern-related terms, which eliminates the need for additional secondary processing when determining the negative-definiteness of derivatives with high-order terms. By combining the high-order two-sided looped-functional with the proposed SCBHII, a stability criterion for SDSs with reduced conservatism is achieved, presented in the form of linear matrix inequalities. The proposed inequality technique and the stability criterion are shown to be effective and superior through three numerical examples and a real-world simplified power market model.

中文翻译：

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基于锯齿特征的递阶积分不等式的采样数据系统稳定性分析


本文的目的是通过引入基于锯齿特征的层次积分不等式（SCBHII）来研究采样数据系统（SDS）的稳定性，并获得维持系统稳定性的最大允许采样周期。首先，通过将SDS中输入延迟的锯齿特性与自由矩阵相关联，提出了SCBHII；它的准确性随着层次结构的增加而提高。随后，引入了同时考虑采样多积分状态和锯齿图案的高阶双边环函数来满足上述不等式。此外，系统变量还通过锯齿模式相关项进行了增强，从而在确定具有高阶项的导数的负定性时无需进行额外的二次处理。通过将高阶两侧环泛函与所提出的 SCBHII 相结合，实现了保守性降低的 SDS 稳定性准则，并以线性矩阵不等式的形式呈现。通过三个数值例子和现实世界的简化电力市场模型，表明所提出的不等式技术和稳定性标准是有效和优越的。