Displacement structure approach to singular root distribution problems: the imaginary axis case

Author

Pal, Debajyoti ; Kailath, Thomas

Author_Institution

Inf. Syst. Res. Lab., AT&T Bell Labs., Holmdel, NJ, USA

Volume

41

Issue

2

fYear

1994

fDate

2/1/1994 12:00:00 AM

Firstpage

138

Lastpage

148

Abstract

A general theory of tabular form root distribution procedures based on LDL* factorization of Bezoutians has been presented in this paper. In particular, we have concentrated on the singular cases arising in the Routh test. A one-to-one correspondence has been established between the rank profile of the underlying Bezoutians and the occurrence of the singular cases. Combining this interpretation with the newly developed factorization procedures of Pal and Kailath (1989), it has been possible to extend the new unified approach of Lev-Ari, Bistritz, and Kailath (1991) to the singular cases. By doing so not only did we obtain all the known procedures but we also obtained new results

Keywords

linear systems; matrix algebra; polynomials; stability; LDL* factorization of Bezoutians; Routh test; displacement structure approach; factorization procedures; imaginary axis case; linear system stability; polynomials; quasi Hankel form; rank profile; singular root distribution problems; singularities; tabular form root distribution procedures; Computer aided software engineering; Costs; Helium; Laboratories; Linear systems; Management information systems; Polynomials; Reflection; Stability; Testing;

fLanguage

English

Journal_Title

Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on

Publisher

ieee

ISSN

1057-7122

Type

jour

DOI

10.1109/81.269050

Filename

269050