You can simply add another constraint to the LMI to impose the constraint.
For instance, assume decision variables are x and y. You are trying to solve;
[10*x^2 -y+2*x ; 6*x y^2] > 0
and you want the -y+2*x to be positive. Then you can add another LMI term
-y + 2*x > 0
or if you want them to be equal to 0, then
-y + 2*x > 0
-y + 2*x < 0
