发表机构
Bernoulli Institute for Mathematics, Computer Science, and Artificial Intelligence, University of Groningen（格罗宁根大学伯努利数学、计算机科学与人工智能研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对耗散线性时不变系统互联，提出统一稳定性定理，通过构造存储函数与耦合二次微分形式之和的Lyapunov函数，推广了静态与动态供给率下的稳定性结果。
AI 中文摘要
耗散性理论能够通过组件的物理特性对复杂互联系统进行稳定性分析。此类稳定性结果的著名例子包括小增益定理和无源定理。在本文中，我们证明了耗散线性时不变（LTI）系统的一个统一稳定性定理。我们采用行为方法，用二次微分形式（QDFs）来表达存储函数和供给率。我们的主要结果为两个LTI行为的互联稳定性建立了条件，这两个行为相对于一般的动态供给率都是耗散的。作为特例，我们恢复了静态供给率的现有结果，例如那些捕获有限$L_2$增益和无源性的结果，以及捕获例如delta耗散性的动态供给率的结果。本文的关键思想是构造一个Lyapunov函数，作为存储函数和耦合QDF之和，从而允许比现有仅处理存储函数之和的工作更丰富的Lyapunov函数类。
英文摘要
Dissipativity theory enables the stability analysis of complex, interconnected systems through the physical properties of their components. Celebrated examples of such stability results include the small gain and passivity theorems. In this paper, we prove a unifying stability theorem for dissipative linear time-invariant (LTI) systems. We use the behavioral approach to express storage functions and supply rates in terms of quadratic differential forms (QDFs). Our main result establishes conditions for the stability of an interconnection of two LTI behaviors that are both dissipative with respect to general, dynamic supply rates. As special cases, we recover existing results for static supply rates, such as those capturing finite $L_2$-gain and passivity, as well as dynamic ones capturing, for example, delta dissipativity. The key idea of the paper is to construct a Lyapunov function as a sum of storage functions and a coupling QDF, thereby allowing for a richer class of Lyapunov functions than existing works dealing with just sums of storage functions.
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