Based on the polyhedral invariant sets, a robust model predictive control algorithm is developed for an input-constrained and output-constrained polytopic linear parameter varying discrete system. A sequence of discrete states converging to the origin is chosen to compute the corresponding state feedback control laws, and also construct each polyhedral invariant sets. At each sampling time, the smallest polyhedral invariant sets that the current measured state can be embedded is determined. The continuous state feedback control laws based on the position of the current measured state between the adjacent polyhedral invariant sets are implemented. Simulation results show that, compared to the ellipsoidal off-line RMPC algorithm, the proposed algorithm yields a substantial expansion of the region stabilized and achieves a less
conservative result.