SIAM Review, Volume 62, Issue 1, Page 3-129, January 2020.
This survey article addresses the class of continuous-time systems where a system modeled by ordinary differential equations is coupled with a static or time-varying set-valued operator in the feedback. Interconnections of this form model certain classes of nonsmooth systems, including sweeping processes, differential inclusions with maximal monotone right-hand side, complementarity systems, differential and evolution variational inequalities, projected dynamical systems, and some piecewise linear switching systems. Such mathematical models have seen applications in electrical circuits, mechanical systems, hysteresis effects, and many more. When we impose a passivity assumption on the open-loop system, and regard the set-valued operator in the feedback as maximally monotone, we obtain a set-valued Lur'e dynamical system. In this article we review the mathematical formalisms, their relationships, main application fields, well-posedness (existence, uniqueness, continuous dependence of solutions), and stability of equilibria. An exhaustive bibliography is provided.

中文翻译：

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结合单调集值算子的动力学系统：形式主义，应用，合理性和稳定性

SIAM评论，第62卷，第1期，第3-129页，2020年1月。
这篇调查文章介绍了连续时间系统的类别，在该系统中，由常微分方程建模的系统在反馈中与静态或时变的设定值算子结合在一起。这种形式的互连模型对某些类别的非光滑系统进行建模，包括清扫过程，右侧具有最大单调的微分包含，互补系统，微分和演化变分不等式，投影动态系统以及某些分段线性切换系统。这样的数学模型已经在电路，机械系统，磁滞效应等中得到了应用。当我们在开环系统上施加无源假设，并将反馈中的设定值算子视为最大单调时，便获得了设定值的Lur'e动力学系统。在本文中，我们回顾了数学形式主义，它们之间的关系，主要应用领域，适定性（存在性，唯一性，解的连续依赖性）以及平衡性的稳定性。提供了详尽的参考书目。