Stability preservation for parametric model order reduction by matrix interpolation

In this thesis the problem of stability preservation for parametric model order reduction by matrix interpolation is investigated. For this purpose the necessary mathematical fundamentals from system theory are given. Furthermore the two most popular model order reduction methods for linear systems are looked at and a brief introduction to various relevant methods for parametric model order reduction is given. The title giving matrix interpolation is analyzed in detail and its various problems, as well as solutions from literature, are studied. Based on these a procedure for the extension of local subspaces is given, whereas for the stability preservation methods known from literature possible problems are shown and new theoretical results are given. As an alternative a novel, flexible method for stability preservation is proposed and its potential pros and cons are shown for two numerical examples.