The main objective of the paper is to present a non-heuristic, mathematically well defined control design to the parallel-type double inverted pendulum. First we apply the recently proposed TP model transformation to generate a finite element convex polytopic representation, namely a Tensor Product model representation (that is equivalent with a kind of TS fuzzy model) of the derived quasi linear parameter varying model of the pendulum system. Then we apply linear matrix inequalities under the parallel distributed compensation control design framework to derive decay rate control with constrain on the control value. Since both steps are executable numerically and automatically one after other, we perform a uniform, tractable and straightforward control design to the pendulum system. In order to validate the resulting controller the paper also presents numerical simulations.