We consider the regulation problem of linear parameter varying systems with input and state constraints. It is assumed that the time-varying parameters are available at the current time, but their future behavior is unknown and contained in a polytopic set. The aim is to design new stabilizing quasi-min-max MPC algorithms based on a nonlinearly parameterized state feedback control law. It is shown that the use of such a control law leads to less conservative results compared to those derived from linearly parameterized state feedback control laws. At each time instant, a convex semi- definite optimization problem is required to solved. Two numerical examples, including a non-quadratically stabilizable system, are given with comparison to earlier solutions from the literature to illustrate the effectiveness of the proposed approaches.