Representation of Solutions to Continuous and Discrete First-Order Linear Matrix Equations With Delay

Asadzade J. A., Mahmudov N.

Mathematical Methods in the Applied Sciences, 2026 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Publication Date: 2026
  • Doi Number: 10.1002/mma.70752
  • Journal Name: Mathematical Methods in the Applied Sciences
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Compendex, INSPEC, MathSciNet, zbMATH
  • Keywords: delay, explicit formula, linear matrix systems, representation of solutions, stability
  • Azerbaijan State University of Economics (UNEC) Affiliated: Yes

Abstract

In this paper, we study continuous and discrete linear delay systems given respectively by (Formula presented.) and its discrete analogue (Formula presented.) where (Formula presented.) are constant non-commuting matrices, and (Formula presented.), (Formula presented.) denote the delay parameters. The main objective is to generalize the classical results of [6, 7] and to provide explicit representations of the solutions. For this purpose, we present generalized delayed exponential-type matrix functions for both continuous and discrete cases. This approach allows us to remove the restrictive commutativity conditions (Formula presented.) and (Formula presented.) imposed in [6, 7], thus obtaining explicit solution formulas for more general classes of systems. Additionally, we establish Ulam-Hyers stability criteria for both continuous and discrete systems, confirming their robustness under small perturbations. The theoretical results are illustrated with numerical examples demonstrating the applicability of the proposed methods.