Specifications of the solution set of parametric generalized Sylvester matrix equations

‎In this work‎, ‎we study the parametric generalized Sylvester matrix equation $\sum_{i=1}^{r} A_{i}(p)X_{i}+\sum_{j=1}^{t} Y_{j}B_{j}(p)=F(p)$ whose elements are linear functions of some parameters‎. ‎This model generalizes both interval generalized Sylvester matrix equations and parametric interval linear systems‎. ‎We first define the concept of AE-solution set for this system and then characterize this solution set‎. ‎The proposed characterizations can be used for constructing some iterative methods for enclosing the solution set of this parametric system‎.