An efficient model predictive controller(MPC) with a time varying terminal constraint set based on N-step
admissible set is developed for a discrete-time linear system with input and state constraints. Firstly, off-line MPC is
designed for an LTI system with input and state constraints by constructing a continuum of polytopic invariant sets. The
terminal constraint set is constructed by the union of these polytopic invariant sets, so this method enlarges the size of
terminal constraint set effectively. In order to enlarge the size of allowable set of initial conditions, a synthesis approach
of on-line and off-line MPC with N-step admissible set is presented. This algorithm not only dramatically reduces on-line
computation but also significantly enlarges the size of the allowable set of initial conditions. The digital simulation results
show the effectivenees of the proposed method.