Typical TP models generated by the TP model transformation are:   Since the TP type polytopic model is a subset of the polytopic model representations, the analysis and design methodologies developed for polytopic representations are applicable for the TP type polytopic models as well. One typical way is to search the nonlinear controller in the form:  where the vertexes formula_39 of the controller is calculated from formula_40. Typically, the vertexes formula_40 are substituted into Linear Matrix Inequalities in order to determine formula_39. In TP type polytopic form the controller is:  where the vertexes formula_44 stored in the core tensor formula_45 are determined from the vertexes formula_46 stored in formula_34. Note that the polytopic observer or other components can be generated in similar way, such as these vertexes are also generated from formula_48. The polytopic representation of a given qLPV model is not invariant. I.e. a given formula_49 has formula_50 number of different representation as:  where formula_52. In order to generate an optimal control of the given model formula_49 we apply, for instance LMIs. Thus, if we apply the selected LMIs to the above polytopic model we arrive at:  Since the LMIs realize a non-linear mapping between the vertexes in formula_48 and formula_56 we may find very different controllers for each formula_52. This means that we have formula_58 different number of "optimal" controllers to the same system formula_49. Thus, the question is: which one of the "optimal" controllers is really the optimal one. The TP model transformation let us to manipulate the weighting functions systematically that is equivalent to the manipulation of the vertexes. The geometrical meaning of this manipulation is the manipulation of the convex hull defined by the vertexes. We can easily demonstrate the following facts:   of a given model formula_49, then we can generate a controller as  then we solved the control problem of all systems formula_63 that can be given by the same vertexes, but with different weighting functions as:  where  If one of these systems are very hardly controllable (or even uncontrollable) then we arrive at a very conservative solution (or unfeasible LMIs). Therefore, we expect that during tightening the convex hull we exclude such problematic systems.