Analysis of Unconstrained Nonlinear MPC Schemes with Time Varying   Control Horizons
  For nonlinear discrete time systems satisfying a controllability condition, we present a stability condition for model predictive control without stabilizing terminal constraints or costs. The condition is given in terms of an analytical formula which can be employed in order to determine a prediction horizon length for which asymptotic stability or a performance guarantee is ensured. Based on this formula a sensitivity analysis with respect to the prediction and the possibly time varying control horizon is carried out. 
Lars Gr\"une, J\"urgen Pannek, Martin Seehafer, Karl Worthmann
math.OC