The paper focuses on the control design of LPV and qLPV models via TS fuzzy model representation and Linear Matrix Inequality (LMI) based design under the Parallel Distributed Compensation control design framework. The related literature reports considerable research on how to manipulate with LMI's to achieve better control performance. This paper shows that this effort is not enough, the optimization of the control performance must include the convex hull manipulation on the TS fuzzy model beside manipulating with the LMIs. The LMI's guaranty the optimal solution for a given convex hull, but the convex hull representation is not invariant. Furthermore, the solutions by LMI's are very sensitive for the convex hull. The paper proposes a systematic concept for various convex hull manipulation method.