标题： 一种耗散性框架用于构建缩放图 显示英文标题

标题： A Dissipativity Framework for Constructing Scaled Graphs

摘要： 缩放相对图最初是在凸优化的背景下引入的，并且最近在控制系统领域受到关注，用于非线性系统的图形分析。 在反馈系统的稳定性分析中，缩放图是一个特别重要的情况，是缩放相对图的一个特例。 在许多方面，缩放图可以被视为线性时不变系统的经典奈奎斯特图的推广，并为分析非线性反馈系统提供了一个强大的图形工具。 然而，在当前的表述中，缩放图需要表征系统对于不可数数量输入的输入输出行为。 这在获取非线性系统的缩放图时构成了一个实际瓶颈，并且目前限制了其应用。 本文提出了一种基于耗散性的框架，用于高效计算几种重要系统类别的缩放图，包括多变量线性时不变系统、脉冲系统和分段线性系统。 所提出的方法利用了线性矩阵不等式、积分二次约束和缩放图之间的新连接，并被证明对于特定的线性时不变系统是精确的。 结果附有多个示例，说明了所提出框架的潜力和有效性。 显示英文摘要

摘要： Scaled relative graphs have been originally introduced in the context of convex optimization and have recently gained attention in the control systems community for the graphical analysis of nonlinear systems. Of particular interest in stability analysis of feedback systems is the scaled graph, a special case of the scaled relative graph. In many ways, scaled graphs can be seen as a generalization of the classical Nyquist plot for linear time-invariant systems, and facilitate a powerful graphical tool for analyzing nonlinear feedback systems. In their current formulation, however, scaled graphs require characterizing the input-output behaviour of a system for an uncountable number of inputs. This poses a practical bottleneck in obtaining the scaled graph of a nonlinear system, and currently limits its use. This paper presents a framework grounded in dissipativity for efficiently computing the scaled graph of several important classes of systems, including multivariable linear time-invariant systems, impulsive systems, and piecewise linear systems. The proposed approach leverages novel connections between linear matrix inequalities, integral quadratic constraints, and scaled graphs, and is shown to be exact for specific linear time-invariant systems. The results are accompanied by several examples illustrating the potential and effectiveness of the presented framework.