# Systems of four coupled one sided Sylvester-type real quaternion matrix equations and their applications

## TL;DR

This paper establishes solvability conditions and general solutions for coupled Sylvester-type quaternion matrix equations, extending existing results and illustrating findings with numerical examples.

## Contribution

It introduces new solvability criteria and explicit solutions for coupled quaternion matrix equations, broadening the theoretical framework in this area.

## Key findings

- Derived necessary and sufficient solvability conditions
- Provided explicit general solutions when solvable
- Extended known results in quaternion matrix equations

## Abstract

In this paper, we derive some necessary and sufficient solvability conditions for some systems of one sided coupled Sylvester-type real quaternion matrix equations in terms of ranks and generalized inverses of matrices. We also give the expressions of the general solutions to these systems when they are solvable. Moreover, we provide some numerical examples to illustrate our results. The findings of this paper extend some known results in the literature.