A triple-mode robust model predictive controller(RMPC) with an enlarging the domain of attraction based on
admissible set is developed for a discrete-time polytopic uncertain linear system with input and state constraints. The
admissible set is used to design this triple-mode RMPC based on the off-line MPC with constructing a continuum of polytopic
invariant sets. In this triple-mode RMPC, the union of the continuum of polytopic invariant sets is treated as mode 1, and
the control admissible set based on ??-step admissible set is treated as mode 2. Combined off-line designing with on-line
optimization, the triple-mode RMPC algorithm with time-varying terminal constraint is presented. This algorithm not only
dramatically reduces on-line computation, but also enlarges the size of the domain of attraction. The digital simulation results
show the effectiveness of the proposed method.