Closed-loop stabilizing model-based predictive control (MPC) algorithms for discrete-time bilinear and state-affine models are presented. Stability of the closed-loop is obtained through the use of an appropriate end-point weighting and end-point inequality constraint. In this way the infinite-horizon performance index is bounded from above by the objective function that is minimized in the MPC algorithm. This paper presents an algorithm that aims at obtaining a large feasibility region by maximizing off-line the region that is defined by the end-point inequality constraint. In order to improve the performance of the MPC algorithm, the conservatism of the upper bound on the infinite-horizon performance index is reduced in the on-line computations.