Benner, Peter : Numerical Linear Algebra for Model Reduction in Control and Simulation

Author(s):

Benner, Peter

Title:

Numerical Linear Algebra for Model Reduction in Control and Simulation

Electronic source:

application/pdf

Preprint series:

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 18, 2005

Mathematics Subject Classification:

65F30			[ Other matrix algorithms ]
93B11			[ System structure simplification ]
41A20			[ Approximation by rational functions ]
65F50			[ Sparse matrices ]

Abstract:

Model reduction is an ubiquitous tool in analysis and simulation of dynamical systems, control design, circuit simulation, structural dynamics, CFD, etc. In the past decades many approaches have been developed for reducing the order of a given model. Often these methods have been derived in parallel in different disciplines with particular applications in mind. We will discuss some of the most prominent methods used for linear systems, compare their properties and highlight similarities. In particular, we will emphasize the role of recent developments in numerical linear algebra in the different approaches. Efficiently using these new techniques, the range of applicability of some of the methods has considerably widened.

Keywords:

model reduction, modal truncation, Pad\'e approximation, balanced truncation, Lyapunov equation, Krylov subspace method

Language:

English

Publication time:

12 / 2005