Summary: FREQUENCY DOMAIN REPRESENTATION AND
SINGULAR VALUE DECOMPOSITION 
A.C. Antoulas
EOLSS Contribution 6.43.13.4
Department of Electrical and Computer Engineering
Rice University
Houston, Texas 77251­1892, USA
e­mail: aca@rice.edu ­ fax: +1­713­348­5686
URL: http://www.ece.rice.edu/”aca
July 29, 2002
Abstract
This contribution reviews the external and the internal representations of linear time­invariant systems. This
is done both in the time and the frequency domains. The realization problem is then discussed. Given the
importance of norms in control design and model reduction, the final part of this contribution is dedicated
to the definition and computation of various norms. Again, the interplay between time and frequency norms
is emphasized.
Key words: linear systems, internal representation, external representation, Laplace transform, Z­transform,
vector norms, matrix norms, Singular Value Decomposition, convolution operator, Hankel operator, reacha­
bility and observability gramians.
 This work was supported in part by the NSF through Grants DMS­9972591 and CCR­9988393.

Source: Antoulas, Athanasios C. - Department of Electrical and Computer Engineering, Rice University

Collections: Engineering