  A typical bottleneck of model predictive control algorithms is the
computational burden in order to compute the receding horizon feedback law
which is predominantly determined by the length of the prediction horizon.
Based on a relaxed Lyapunov inequality we present techniques which allow us to
show stability and suboptimality estimates for a reduced prediction horizon. In
particular, the known structural properties of suboptimality estimates based on
a controllability condition are used to cut the gap between theoretic stability
results and numerical observations.
