$A $, $ C$ $(n,n)$ are symmetric  PSD  matrices, 
$B$ is PD symmetric matrix, and  $H_i$ $\; $ $(i=[1,m])$ represent $ m $ complex   matrices. $H_i$  are all one rank matrix

 Our objectif is to find PSD matrix X that enable:

$A\sum\limits_{i = 1}^{m - 1} {{H_i}(B + X){H_i} + A(X + B) + {H_m}(B + X) = C}$