Skip Navigation

IMA Journal of Mathematical Control and Information 2001 18(2):129-151; doi:10.1093/imamci/18.2.129
© 2001 by Institute of Mathematics and its Applications
This Article
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Tan, L.
Right arrow Articles by Pugh, A. C.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

A novel method to determine the finite and infinite frequency structure of a rational matrix

Liansheng Tan1 and A. C. Pugh1

1 Department of Mathematical Sciences, Loughborough University, Loughborough, Leicestershire, LE11 3TU, UK. Email: A.C.Pugh@lboro.ac.uk

A novel method is proposed for determining the finite and infinite frequency structure of any rational matrix. For a polynomial matrix, a natural relationship between the rank information of the Toeplitz matrices and the number of corresponding irreducible elementary divisors in its Smith form is established. These special Toeplitz matrices are constructed from certain derivatives evaluated at the Smith zeros of the matrix. For a rational matrix, this technique can be employed efficiently to find its infinite frequency structure by examining the finite frequency structure of the dual of its companion polynomial matrix. This is extended to find the finite frequency structure of a rational matrix via a polynomial matrix fraction description. Some neat and numerically stable algorithms are developed.

Keywords: polynomial matrix; Toeplitz matrix; irreducible elementary divisor; Smith form; Smith–; McMillan form at infinity; polynomial matrix fraction description.


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer:
Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.