  We provide a stability and performance analysis for nonlinear model
predictive control (NMPC) schemes subject to input constraints. Given an
exponential stabilizability and detectability condition w.r.t. the employed
state cost, we provide a sufficiently long prediction horizon to ensure
asymptotic stability and a desired performance bound w.r.t. the
infinite-horizon optimal controller. Compared to existing results, the provided
analysis is applicable to positive semi-definite (detectable) cost functions,
provides tight bounds using a linear programming analysis, and allows for a
seamless integration of general positive-definite terminal cost functions in
the analysis. The practical applicability of the derived theoretical results
are demonstrated with numerical examples.
