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Approximating the solutions of Lyapunov equations for balanced truncation

Gonzalez, Stephanie (2018) Approximating the solutions of Lyapunov equations for balanced truncation. Bachelor's Thesis, Mathematics.


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Model reduction approximates a high-order system by one of lower-order and is often necessary for simulation and control of large-scale systems to be feasible. A popular method of model reduction is balanced truncation, since it preserves stability of the original model and has a computable error bound. However, balanced truncation involves solving Lyapunov equations, which are unfeasible to solve exactly for systems of orders larger than 10^3. In this paper, methods for approximating the solutions, which would make balanced truncation applicable to high-order models, are discussed and compared. The methods considered are the regular and extended Krylov subspace methods of Y. Saad and V. Simoncini, respectively. Theoretical discussions and numerical experiments are used to compare their convergence rates and suitability for balanced truncation. Numerical experiments demonstrate faster convergence for the extended Krylov subspace method than the regular Krylov subspace method. Futhermore, balanced truncation, when using the extended Krylov subspace method, shows increased accuracy in approximating the original model than when using the regular Krylov subspace method. The approximation accuracy shows to be particularly increased for low frequency inputs with the extended rather than the regular Krylov subspace method.

Item Type: Thesis (Bachelor's Thesis)
Supervisor name: Besselink, B. and Wubs, F.W.
Degree programme: Mathematics
Thesis type: Bachelor's Thesis
Language: English
Date Deposited: 24 Apr 2018
Last Modified: 01 May 2018 14:49

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