Model Order Reduction via Moment-Matching: A State of the Art Review

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.