  This paper presents a stability analysis tool for model predictive control
(MPC) where control action is generated by optimising a cost function over a
finite horizon. Stability analysis of MPC with a limited horizon but without
terminal weight is a well known challenging problem. We define a new value
function based on an auxiliary one-step optimisation related to stage cost,
namely optimal one-step value function (OSVF). It is shown that a finite
horizon MPC can be made to be asymptotically stable if OSVF is a (local)
control Lyapunov function (CLF). More specifically, by exploiting the CLF
property of OSFV to construct a contractive terminal set, a new stabilising MPC
algorithm (CMPC) is proposed. We show that CMPC is recursively feasible and
guarantees stability under the condition that OSVF is a CLF. Checking this
condition and estimation of the maximal terminal set are discussed. Numerical
examples are presented to demonstrate the effectiveness of the proposed
stability condition and corresponding CMPC algorithm.
