ABSTRACT
Modeling of physical systems usually results in complex high-order models, and it is often desirable to replace these models with simpler reduced-order models without significant error. The model order reduction problem consists of approximating a high-order system G by a lower-order system G ^ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315136523/da37a17e-5c01-4454-a3c1-f35b8dae80d3/content/inequ8_1.tif"/> according to some given criterion. In this chapter, necessary and sufficient conditions are derived for the solution of the https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315136523/da37a17e-5c01-4454-a3c1-f35b8dae80d3/content/inequ4a_7.tif"/> and the covariance bounded model reduction problems using a linear matrix inequality formulation. These approaches are consistent with the algebraic emphasis of this book. However, many other model reduction methods can be found in the literature, e.g. see [21, 125, 74, 145, 22, 91, 5, 73, 39, 27, 81].
