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Approximation of linear dynamical systems \Lambda A.C. Antoulas

Summary: Approximation of linear dynamical systems \Lambda
A.C. Antoulas
Department of Electrical and Computer Engineering
Rice University
Houston, Texas 77251­1892
E­mail: acarice.edu ­ Fax: +1­713 524­5237
March 2, 1998
Approximation is an important issue in the theory and practice of dynamical systems. In this
essay we will review a theory of approximation of linear dynamical systems which has two im­
portant properties. First, it preserves stability and second, explicit a priori bounds for the norm
of the error can be derived. Main ingredients of this theory are: the 2­norms used to measure the
quantities involved, in particular the Hankel norms, the infinity norms, and a set of invariants
called the Hankel singular values. The main tool for the construction of approximants is the
all­pass dilation.
Keywords: linear systems, approximation, 2­norms, infinity norm, Hankel operator, Hankel
singular values, balancing, balanced truncation, Lyapunov equations, all­pass systems, all­pass
\Lambda This is article #1049, prepared for the Encyclopedia of Electrical and Electronics Engineering, edited
by J.G. Webster, published by John Wiley and Sons, Inc.


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


Collections: Engineering