Summary of recent results on the decay rate of the Hankel singular values

Author

Antoulas, A.C.

Author_Institution

Dept. of Electr. & Comput. Eng., Rice Univ., Houston, TX, USA

Volume

4

fYear

2001

fDate

2001

Firstpage

3655

Abstract

The purpose of the paper is to investigate the issue of the decay rate of the Hankel singular values of a linear system. This issue is of considerable interest in model reduction, by means of balanced truncation for instance, since the sum of the neglected singular values provides an upper bound for an appropriate norm of the approximation error. The decay rate involves a new set of invariants associated with a linear system, which are obtained by evaluating a modified transfer function at the poles of the system

Keywords

Lyapunov methods; eigenvalues and eigenfunctions; linear systems; matrix algebra; multidimensional systems; poles and zeros; reduced order systems; transfer functions; Cauchy matrix; Hankel operator; Hankel singular values; Lvapunov equations; approximation error; balanced truncation; decay rate; finite-dimensional time-invariant system; linear system; majorization; model reduction; modified transfer function; neglected singular values; poles; upper bound; Approximation error; Ear; Eigenvalues and eigenfunctions; Equations; Large-scale systems; Linear systems; Reduced order systems; Transfer functions; Uniform resource locators; Upper bound;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 2001. Proceedings of the 40th IEEE Conference on

Conference_Location

Orlando, FL

Print_ISBN

0-7803-7061-9

Type

conf

DOI

10.1109/.2001.980428

Filename

980428