Balanced realizations of finite dimensional time invariant dynamical systems

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2021
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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.

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Fachgebiet (DDC)
510 Mathematik
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Balanced realizations of FDLTI, block Krylov methods for solving large Lyapunov equations
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ISO 690THIELE, Michael, 2021. Balanced realizations of finite dimensional time invariant dynamical systems [Bachelor thesis]. Konstanz: Universität Konstanz
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@mastersthesis{Thiele2021Balan-54846,
  year={2021},
  title={Balanced realizations of finite dimensional time invariant dynamical systems},
  address={Konstanz},
  school={Universität Konstanz},
  author={Thiele, Michael}
}
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Konstanz, Universität Konstanz, Bachelorarbeit, 2021
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