1. Mathematical background and introductory examples

The approximation, or reduction, of high-dimensional dynamic models is a very broad subject, which in reality covers a wide range of issues. In particular, depending on the nature of the models considered (linear, second-order, etc.), the concepts and methods can be very different. This article focuses on the approximation of linear dynamic models. This may seem restrictive, but these models are widely used in industry because, on the one hand, they are often rich enough to faithfully represent the behavior of many physical systems around an operating point, and on the other hand, they are simple to use for simulation or control. Furthermore, with this class of models, very powerful mathematical tools can be used to evaluate the errors introduced during approximation.

The mathematical formulations of the problems considered are set out in section