  We are concerned with the design of Model Predictive Control (MPC) schemes
such that asymptotic stability of the resulting closed loop is guaranteed even
if the linearization at the desired set point fails to be stabilizable.
Therefore, we propose to construct the stage cost based on the homogeneous
approximation and rigorously show that applying MPC yields an asymp-totically
stable closed-loop behavior if the homogeneous approximation is asymptotically
null controllable. To this end, we verify cost controllability-a condition
relating the current state, the stage cost, and the growth of the value
function w.r.t. time-for this class of systems in order to provide stability
and performance guarantees for the proposed MPC scheme without stabilizing
terminal costs or constraints.
