  We present a novel nonlinear model predictive control (MPC) scheme with
relaxed stability criteria, based on the idea of generalized discrete-time
control Lyapunov functions. These functions need to satisfy an average descent
over a finite window of time, rather than a descent at every time step. One
feature of this scheme is that it allows for implementing a flexible number of
control inputs in each iteration, in a computationally attractive manner, while
guaranteeing recursive feasibility and stability. The benefits of our
flexible-step implementation are also demonstrated in an application to
nonholonomic systems, where the one-step standard implementation may suffer
from lack of asymptotic convergence.
