IDEAS home Printed from https://ideas.repec.org/a/taf/tsysxx/v42y2011i8p1293-1303.html
   My bibliography  Save this article

Block checker/diagonal transformation matrices, their properties, and the interplay with fast-lifting

Author

Listed:
  • Tomomichi Hagiwara

Abstract

This article introduces what we call block checker matrices with some specific structures characterised by a set of integers, and then introduces the permutation matrices called block checker/diagonal (BCD) transformation matrices that relate block checker matrices with block diagonal matrices through similarity transformations. The study is motivated by the importance of the fast-lifting technique in control theory, especially in the study of sampled-data systems and time-delay systems. More precisely, it is partly motivated by the desire for alleviating the bother of describing the class of the matrices commuting with block diagonal matrices, and for such a purpose the permutation with BCD transformation matrices is helpful. The study further extends to investigating the various useful properties among BCD transformation matrices, as well as their interplay relations with various variants of fast-lifting, e.g. full-vector fast-lifting and subvector-wise fast-lifting, or one-stage fast-lifting and two-stage fast-lifting. The usefulness of the results in the context of the fast-lifting treatment is also suggested.

Suggested Citation

  • Tomomichi Hagiwara, 2011. "Block checker/diagonal transformation matrices, their properties, and the interplay with fast-lifting," International Journal of Systems Science, Taylor & Francis Journals, vol. 42(8), pages 1293-1303.
    • Handle: RePEc:taf:tsysxx:v:42:y:2011:i:8:p:1293-1303
    DOI: 10.1080/00207721.2010.496057
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/00207721.2010.496057
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/00207721.2010.496057?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:taf:tsysxx:v:42:y:2011:i:8:p:1293-1303. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/TSYS20 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.