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

Nazim I. Mahmudov (), Muath Awadalla () and Meraa Arab
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Nazim I. Mahmudov: Department of Mathematics, Eastern Mediterranean University, T.R. North Cyprus Mersin 10, Famagusta 99628, Turkey
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

Mathematics, 2025, vol. 13, issue 6, 1-24

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.

Keywords: second-order difference; Z transform; iterative learning control (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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