Low rank solution

Does CVX have internal way to find the lowest rank solution of a problem? I want to see if my solution is unique or it is the CVX that choose the lowest rank matrix among the available solutions ?

Rank constraints are not convex, and they cannot be expressed using mixed-integer constraints, either.

Perhaps I was not clear enough, I am solving a convex optimization problem using CVX and I always get a low rank solution. I wanted to see if this comes from my model or the solver somehow helps to give me the low rank solution?

Certain models do tend to low rank solutions, and there are certain theoretical results in literature that illuminate why this is sometimes the case. But CVX does nothing specifically to bring this about.