The paper shows that the separated structure of parameter dependencies within the Polytopic Tensor-Product (TP) model can be exploited during the controller design by applying controller candidates that depend only on certain parameter sets. This approach combines the polytopic uncertainty and Parallel Distributed Compensation (PDC) concepts in such a way that they become special cases of the proposed formulation. Motivated by this recognition and the fact that the separation of parameter dependencies increases the complexity and computational cost, the definition of Polytopic TP representation for LPV/qLPV models is relaxed. The new definition allows for the use of arbitrarily chosen parameter sets in the model - according to the control goals - and the separation can be performed only for these sets. Through the derivation, an appropriate transformation algorithm and the unique Affine TP model is introduced discussing the related concepts of tensor algebra and affine geometry as well.