The dissipativity concept sits at the intersection of physics, systems theory, and control engineering as a natural generalization of passive systems that dissipate energy. It relates the external behavior of systems to their internal state and connects the subjects of optimal control, algebraic Riccati equations, linear matrix inequalities, complex functions, and spectral factorization. Within control, its applications include the analysis and design of interconnected systems (such as cyberphysical systems), robustness, and the absolute stability problem as well as network synthesis (of electrical, mechanical, and multiphysics systems). Dissipativity emerged as a stand-alone concept following the seminal “Dissipative Dynamical Systems” articles of Jan Willems, which drew on the work of Kalman, Youla, Anderson, Yakubovich, Popov, and others. This article details recent developments in the treatment of dissipativity and the related concept of reciprocity for systems that are not necessarily controllable and need not lend themselves naturally to an input–state–output perspective, as is the case for many physical and passive systems. We illustrate these concepts using simple electric circuit and mechanical network examples. We also draw inspiration from the behavioral theory developed by Jan Willems and collaborators, a natural formalism for analyzing physical systems that need not be controllable and characterized in terms of inputs and outputs.

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耗散性、互易性和无源网络综合：从 Jan Willems 的开创性耗散动力系统文章到今天

耗散性概念位于物理学、系统理论和控制工程的交叉点，是耗散能量的无源系统的自然概括。它将系统的外部行为与其内部状态联系起来，并将最优控制、代数 Riccati 方程、线性矩阵不等式、复函数和谱分解等主题联系起来。在控制范围内，它的应用包括互连系统（例如信息物理系统）的分析和设计、鲁棒性和绝对稳定性问题以及网络综合（电气、机械和多物理系统）。在 Jan Willems 的开创性“耗散动力系统”文章之后，耗散性作为一个独立的概念出现，该文章借鉴了 Kalman、Youla、Anderson、Yakubovich、Popov 等人的工作。本文详细介绍了耗散性处理的最新进展以及相关系统的互惠概念，这些系统不一定是可控的，并且不需要自然地适应输入-状态-输出的角度，就像许多物理和无源系统的情况一样。我们使用简单的电路和机械网络示例来说明这些概念。我们还从 Jan Willems 及其合作者开发的行为理论中汲取灵感，这是一种自然的形式主义，用于分析不需要根据输入和输出进行控制和表征的物理系统。就像许多物理和被动系统一样。我们使用简单的电路和机械网络示例来说明这些概念。我们还从 Jan Willems 及其合作者开发的行为理论中汲取灵感，这是一种自然的形式主义，用于分析不需要根据输入和输出进行控制和表征的物理系统。就像许多物理和被动系统一样。我们使用简单的电路和机械网络示例来说明这些概念。我们还从 Jan Willems 及其合作者开发的行为理论中汲取灵感，这是一种自然的形式主义，用于分析不需要根据输入和输出进行控制和表征的物理系统。