I don’t understand exactly what you’re asking, and I suspect no one else really would, either.
Nevertheless, you are apparently seeking modeling advice of a type not appropriate for this forum. if you get to the point of having a convex LMI or other optimization or feasibility model which deals with any uncertainty only within the context of one or more “deterministic” problems,l and need help in how to use CVX to handle it, then please feel free to request such assistance at that time.
Keep in mind, per Question about convex optimization , you can not use ureal from Robust Control Toolbox within CVX. You will have to to figure pout how to deal with uncertainty in an appropriate way, whether that ultimately involves using CVX or not.