I won’t address what should or shouldn’t converge to what.
However, are you sure you are even specifying semidefinite constraints? Specifically, what guarantees that X*P is symmetric? You haven;t declared P to be symmetric (recall your previous thread LMI formulation using Yalmip vs CVX ), and I have no idea what (the numerical value of ) X is. Did you get a warning about asymmetry?
You mkay be better off at a different forum for a discussion of what should converge to what.