IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v13y2025i6p916-d1609175.html
   My bibliography  Save this article

Explicit Form of Solutions of Second-Order Delayed Difference Equations: Application to Iterative Learning Control

Author

Listed:
  • Nazim I. Mahmudov

    (Department of Mathematics, Eastern Mediterranean University, T.R. North Cyprus Mersin 10, Famagusta 99628, Turkey
    Research Center of Econophysics, Azerbaijan State University of Economics (UNEC), Istiqlaliyyat Str. 6, Baku 1001, Azerbaijan)

  • Muath Awadalla

    (Department of Mathematics and Statistics, College of Science, King Faisal University, Hofuf 31982, Al Ahsa, Saudi Arabia)

  • Meraa Arab

    (Department of Mathematics and Statistics, College of Science, King Faisal University, Hofuf 31982, Al Ahsa, Saudi Arabia)

Abstract

A system of inhomogeneous second-order difference equations with linear parts given by noncommutative matrix coefficients are considered. The closed form of its solution is derived by means of a newly defined delayed matrix sine/cosine using the Z transform and determining function. This representation helps with analyzing iterative learning control by applying appropriate updating laws and ensuring sufficient conditions for achieving asymptotic convergence in tracking.

Suggested Citation

  • Nazim I. Mahmudov & Muath Awadalla & Meraa Arab, 2025. "Explicit Form of Solutions of Second-Order Delayed Difference Equations: Application to Iterative Learning Control," Mathematics, MDPI, vol. 13(6), pages 1-24, March.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:6:p:916-:d:1609175
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/13/6/916/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/13/6/916/
    Download Restriction: no
    ---><---

    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:gam:jmathe:v:13:y:2025:i:6:p:916-:d:1609175. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.