Spectral factorization by symmetric extraction for a vibrating string with low damping

Author

Callier, F.M. ; Winkin, Joseph J.

Author_Institution

Dept. of Math., Namur Univ., Belgium

Volume

2

fYear

2003

fDate

9-12 Dec. 2003

Firstpage

1854

Abstract

One considers the method of spectral factorization, (J. Winkin et al., 2002; F.M. Callier et al., 1992; F.M. Callier et al., 1990), for a scalar coercive spectral density in the framework of the Callier-Desoer algebra of distributed parameter system transfer functions and the context of LQ-optimal control. This method is applied to a vibrating string with low damping. The latter is reported to satisfy the convergence criteria of the method, which are known to hold for a class of semigroup Hubert state-space systems with a Riesz-spectral generator. Moreover numerical results are given and commented with respect to the observed slow speed of convergence.

Keywords

Hilbert spaces; algebra; convergence; damping; distributed parameter systems; eigenvalues and eigenfunctions; linear quadratic control; matrix decomposition; multidimensional systems; state-space methods; transfer functions; vibration control; vibrations; Callier-Desoer algebra; Hubert state-space systems; Riesz-spectral generator; convergence criteria; distributed parameter system; eigenvalues; infinite dimensional systems; linear quadratic control; low damping; optimal control; spectral density; spectral factorization; symmetric extraction; transfer functions; vibrating string; Algebra; Context modeling; Convergence of numerical methods; Damping; Feedback control; Mathematics; Optimal control; Spectral analysis; System analysis and design; Transfer functions;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 2003. Proceedings. 42nd IEEE Conference on

ISSN

0191-2216

Print_ISBN

0-7803-7924-1

Type

conf

DOI

10.1109/CDC.2003.1272883

Filename

1272883