## Balanced realizations of finite dimensional time invariant dynamical systems

2021
Bachelor thesis
Published
##### Abstract
In this thesis we demonstrate, how to receive a balanced realization of a finite dimensional linear time invariant (FDLTI) dynamical system. For that purpose we use the discretized heat equation as an application. We get such a balanced realization by following the algorithms in Robust and Optimal Control. So first we make the system observable, by applying one such algorithm and afterwards we make it controllable with a dual one. Then we have a minimal realization. From this point on we can apply a balancing algorithm to get a balanced realization. An important role in these algorithms plays the Lyapunov equation. In the controllability as well as the observability algorithm, we start by solving a Lyapunov equation. For these equations, we implemented the Lyapunov solver presented in Krylov subspace methods for large Lyapunov equations. This Lyapunov solver is based on a low rank block Krylov approximation. The way to a balanced realization connects this Lyapunov solver with the well known control theory of FDLTI dynamical systems.
510 Mathematics
##### Keywords
Balanced realizations of FDLTI, block Krylov methods for solving large Lyapunov equations
##### Cite This
ISO 690THIELE, Michael, 2021. Balanced realizations of finite dimensional time invariant dynamical systems [Bachelor thesis]. Konstanz: Universität Konstanz
BibTex
@mastersthesis{Thiele2021Balan-54846,
year={2021},
title={Balanced realizations of finite dimensional time invariant dynamical systems},
school={Universität Konstanz},
author={Thiele, Michael}
}

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