In polytopic model-based controller synthesis, the vertices of the model determine the achievable performance characteristics. This paper introduces a new concept, that allows for the sophisticated construction of non-simplex enclosing polytopes. The non-simplex structures in general, have much better descriptor properties than the simplex one that leads to less conservative synthesis. The paper demonstrates the workflow of controller design for a nonlinear system through the example of the TORA (Translational Oscillator with a Rotational Actuator) system. The numerical results clearly show that the proposed approach is capable of excluding non-stabilizable regions located between the exact convex hull and the enclosing simplex. The non-simplex polytope leads to an increased number of vertices but it practically does not influence the viability of Tensor-Product (TP) formalization and the feasibility of controller design while the achievable control performance can be improved significantly.