Thread Subject: Help with LMI

Hello all,
Does anyone know how to transform a set of constraints of the form
I+BX>=0
BXg<=0
into a LMI form (LMI problem) . where the matrix X is the variable to be calculated, and B is a known matrix, and g is a known vector.
I want to do that because i have a problem that contains in addition to the above two contraintes a set of LMIs. So the aim is to find the matrix X that satisfies both the contraintes and the LMI inequalities. Thus, if i transformed the above constraintes into a LMI inequalities then my problem becomes a LMI problem that can be solved by LMI toolbox solver.
Has anyone an idea about this problem or a better idea about its solution?

Thanks in advance
David