耗散性、互易性与无源网络综合：从 Jan Willems 的开创性论文《Dissipative Dynamical Systems》到当今
Dissipativity, reciprocity and passive network synthesis: from Jan Willems' seminal Dissipative Dynamical Systems papers to the present day
AI总结：
本文综述耗散性与互易性理论的最新进展，将其推广到不可控、非输入-状态-输出描述的物理无源系统，并以电路和机械网络示例说明其在网络综合中的应用。
摘要：
耗散性概念处于物理学、系统理论和控制工程的交汇处，是耗散能量的无源系统的自然推广。它将系统的外部行为与其内部状态联系起来，并连接了最优控制、代数 Riccati 方程、线性矩阵不等式、复函数和谱分解等主题。在控制领域，其应用包括互联系统（如信息物理系统）的分析与设计、鲁棒性和绝对稳定性问题，以及（电气、机械和多物理系统的）网络综合。本文详细介绍了在处理不一定可控、也不必自然适合输入-状态-输出视角的系统时，耗散性及相关互易性概念研究的最新进展，许多物理系统和无源系统正是这种情况。我们通过简单的电路和机械网络示例来说明这些概念。
英文摘要：
The dissipativity concept sits at the intersection of physics, systems theory, and control engineering, as a natural generalisation 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 cyber-physical systems), robustness, and the absolute stability problem, and network synthesis (of electrical, mechanical, and multi-physics systems). 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.
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