  In this paper, we provide a stability and performance analysis of model
predictive control (MPC) schemes based on finite-tail costs. We study the MPC
formulation originally proposed by Magni et al. (2001) wherein the standard
terminal penalty is replaced by a finite-horizon cost of some stabilizing
control law. In order to analyse the closed loop, we leverage the more recent
technical machinery developed for MPC without terminal ingredients. For a
specified set of initial conditions, we obtain sufficient conditions for
stability and a performance bound in dependence of the prediction horizon and
the extended horizon used for the terminal penalty. The main practical benefit
of the considered finite-tail cost MPC formulation is the simpler offline
design in combination with typically significantly less restrictive bounds on
the prediction horizon to ensure stability. We demonstrate the benefits of the
considered MPC formulation using the classical example of a four tank system.
