IDEAS home Printed from https://ideas.repec.org/a/taf/tsysxx/v56y2025i10p2221-2230.html
   My bibliography  Save this article

Stabilisation in an infinite time horizon by homomorphically encrypted first-order controllers with regular Pisot poles

Author

Listed:
  • Mohammad Saleh Tavazoei

Abstract

It has been previously found that partially homomorphic encryption based controllers cannot operate in an infinite time horizon, unless all elements of their state matrices are integer numbers. Considering this fact and the results of a recent research revealing the role of Pisot numbers to act as the poles of integer state matrix based state space models involving no unstable pole-zero cancellation, the present paper aims to introduce some classes of realisations implementing first-order discrete-time controllers, which can be used in an infinite time horizon in encrypted control systems. These classes of controller realisations are obtained based on sequences approaching to limit points of positive Pisot numbers settled in the range $ (1,2) $ (1,2). An analytical procedure is also suggested to find the exact range of the controller gain for ensuring the closed-loop stability.

Suggested Citation

  • Mohammad Saleh Tavazoei, 2025. "Stabilisation in an infinite time horizon by homomorphically encrypted first-order controllers with regular Pisot poles," International Journal of Systems Science, Taylor & Francis Journals, vol. 56(10), pages 2221-2230, July.
    • Handle: RePEc:taf:tsysxx:v:56:y:2025:i:10:p:2221-2230
    DOI: 10.1080/00207721.2024.2441454
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/00207721.2024.2441454
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/00207721.2024.2441454?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:56:y:2025:i:10:p:2221-2230. 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.