Work

Analytical Solutions and Controllability of Delay Differential Matrix Equations via Kronecker Product and Delayed Matrix Functions

Year: 2025

Type: article

Abstract: This work introduces a unified framework for analyzing linear delay differential Sylvester matrix equations with noncommuting coefficients. The methodology employs a Kronecker product-based vectorization to transform the system, yielding explicit closed-form solutions via a novel delayed perturbation matrix function. Additionally, a delay-adapted Gramian matrix is formulated to derive necessary and sufficient controllability criteria. The approach’s efficacy is confirmed through a numerical example, demonstrating its capability in complex, noncommutative scenarios where classical methods are inapplicable.

Source: Mathematics

DOI: 10.3390/math13223581

Authors: Fatemah Mofarreh, Faridah Alruwaili, Xingtao Wang, Ahmed M. Elshenhab

Institutions: Princess Nourah bint Abdulrahman University, Harbin Institute of Technology, Mansoura University

Language: English

Topic: Nonlinear Differential Equations Analysis

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,137

Funder: Princess Nourah Bint Abdulrahman University