The past few decades have seen a significant spurt in developing lower-order, parsimonious models of large-scale dynamical systems used for design and control. These surrogate models effectively capture the most interesting dynamic features of the full-order models (FOMs) while preserving the input–output relation. Model order reduction (MOR) techniques have intensively been further developed to treat increasingly complex, multi-resolution models spanning a thousand degrees of freedom. This manuscript presents a state-of-the-art review of the moment-matching based order reduction methods for linear and nonlinear dynamical systems. We track the progress of moment-matching methods from their inception to how they have emerged as the most commonly adopted platform for reducing systems in large-scale settings. We discuss the frequency and time-domain notions of moment-matching between the original and reduced models. Moreover, we also provide some new results highlighting the extensive applications of this technique in reducing micro-electro-mechanical systems.

在过去的几十年里，在开发用于设计和控制的大规模动态系统的低阶简约模型方面取得了重大进展。这些代理模型有效地捕获了全阶模型 (FOM) 最有趣的动态特征，同时保留了输入-输出关系。模型降阶 (MOR) 技术已得到深入发展，以处理跨越一千个自由度的日益复杂的多分辨率模型。这份手稿对线性和非线性动态系统的基于矩匹配的阶数减少方法进行了最先进的审查。我们跟踪矩匹配方法的进展，从它们开始到它们如何成为最常用的用于减少大规模环境中的系统的平台。我们讨论了原始模型和简化模型之间矩匹配的频域和时域概念。此外，我们还提供了一些新结果，突出了该技术在减少微机电系统方面的广泛应用。