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

Mahmudov N., Awadalla M., Arab M.

Mathematics, vol.13, no.6, 2025 (SCI-Expanded, Scopus) identifier

  • Nəşrin Növü: Article / Article
  • Cild: 13 Say: 6
  • Nəşr tarixi: 2025
  • Doi nömrəsi: 10.3390/math13060916
  • jurnalın adı: Mathematics
  • Jurnalın baxıldığı indekslər: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Açar sözlər: iterative learning control, second-order difference, Z transform
  • Açıq Arxiv Kolleksiyası: Məqalə
  • Adres: Yox

Qısa məlumat

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 (Formula presented.) 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.