Model reduction (also called system reduction, order reduction) is an ubiquitous tool in the analysis and simulation of dynamical systems, control design, circuit simulation, structural dynamics, CFD, etc. In the past decades many approaches have been developed for reducing the complexity of a given model. In this introductory talk, we will survey some of the most prominent methods used for linear systems, compare their properties and highlight similarities. In particular, we will emphasize the role of recent developments in numerical linear algebra in the different approaches. Efficiently using these techniques, the range of applicability of some of the methods has considerably widened.
The performance of several approaches will be demonstrated using real-world examples from a variety of engineering disciplines.