  In this note, a new formulation of Model Predictive Control (MPC) framework
with no stability-related terminal constraint is proposed and its stability is
proved under mild standard assumptions. The novelty in the formulation lies in
the use of time-varying monotonically increasing stage cost penalty. The main
result is that the $0$-reachability prediction horizon can always be made
stabilizing provided that the increasing rate of the penalty is made
sufficiently high.
