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Tobias Damm: Lehre/Teaching, Winter 10/11
Lecture: Numerical methods in Control Theory
Course Description
The focus is on numerical linear algebra applied to problems in control theory. Many questions in linear control theory require the computation of eigenvalues (e.g. stability), rank estimations (e.g. controllability) or the solution of matrix equations (in particular Lyapunov and Riccati equations).
Major topics are model order reduction and the solution of Riccati equations.
Singular values and eigenvalues
Krylov subspace methods
Model order reduction
Linear matrix equations
Riccati equations
Lecture Notes
work in progress, version 19.11.10
Exercises
From time to time we will discuss problems during the lectures.
Literature
Major source
- A.C. Antoulas: Approximation of Large-Scale Dynamical Systems
Other recommended books
- J. Demmel: Applied Numerical Linear Algebra
- L.N. Trefethen, D. Bau: Numerical Linear Algebra
- L.N. Trefethen, M. Embree: Spectra and Pseudospectra
- A. Linnemann: Numerische Methoden für lineare Regelungssysteme
- D. Hinrichsen, A.J. Pritchard: Mathematical Systems Theory I
- P. Lancaster, L. Rodman: The Algebraic Riccati Equation
Internet sources:
- V. Mehrmann: Kontrolltheorie
- E. Sontag: Mathematical Control Theory
- Numerical Computing with MATLAB by C. Moler
- Books by Y. Saad, namely:
Iterative Methods for Sparse Linear Systems,
Numerical Methods for Large Eigenvalue Problems
- Barrett, Berry, Chan, Demmel, Donato, Dongarra, Eijkhout, Pozo, Romine, van der Vorst, Templates for the solution of linear systems
- A.C. Antoulas, D. Sorensen: Approximation of large-scale dynamical systems: An overview
- A.C. Antoulas, D. Sorensen, S. Gugercin: A survey of model reduction methods for large-scale systems
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