The concept of dissipativity, as introduced by Jan Willems, is one of the cornerstones of systems and control theory. Typically, dissipativity properties are verified by resorting to a mathematical model of the system under consideration. This article aims to assess dissipativity using computing storage functions for linear systems directly from measured data. As our main contributions, we provide conditions under which dissipativity can be ascertained from a finite collection of noisy data samples. Three different noise models are considered that can capture a variety of situations, including the cases where the data samples are noise-free, the energy of the noise is bounded, or the individual noise samples are bounded. All conditions are phrased in terms of data-based linear matrix inequalities, which can be readily solved using existing software packages.

中文翻译：

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数据驱动的耗散分析：矩阵 S-引理的应用

Jan Willems 介绍的耗散性概念是系统和控制理论的基石之一。通常，通过求助于所考虑系统的数学模型来验证耗散特性。本文旨在直接从测量数据中使用线性系统的计算存储函数来评估耗散性。作为我们的主要贡献，我们提供了可以从有限的噪声数据样本集合中确定耗散性的条件。考虑了三种不同的噪声模型，它们可以捕获各种情况，包括数据样本无噪声、噪声能量有界或单个噪声样本有界的情况。所有条件都用基于数据的线性矩阵不等式来表述，