# Ingvar Ziemann: Model Reduction of Semistable In finite-Dimensional Control Systems

**Time: **
Thu 2018-06-14 10.00 - 11.00

**Location: ** Room 14, House 5, Kräftriket, Department of Mathematics, Stockholm University

**Doctoral student: **
Ingvar Ziemann (MSc student)

**Supervisor: **
Yishao Zhou

Abstract: In this thesis, we extend parts of the framework available for model reduction of finite-dimensional stable control systems to an infinite-dimensional and semistable setting. To achieve our goals, we build upon earlier work in which Hardy-2-norm error estimates for the model reduction of finite-dimensional systems driven by a graph Laplacian are established. The difference between this and previous work is threefold: First, we consider infinite-dimensional systems as to include systems driven by Partial Differential Operators and we thus place earlier work in an appropriate Functional-Analytic setting. Second, we consider a broader class of exponentially semistable systems, not just those driven by a graph Laplacian. Third, we restrict to a class of model reductions which have a dynamic invariance with respect to their kernel and the semigroup associated to the system. For completeness, we also give a brief introduction to Semigroup Theory and provide background material from Functional Analysis. Throughout the text, the second derivative operator and heat equation on on the unit interval are used as examples.