  In this work, we establish different control design approaches for
discrete-time systems, which build upon the notion of finite-step control
Lyapunov functions (fs-CLFs). The design approaches are formulated as
optimization problems and solved in a model predictive control (MPC) fashion.
In particular, we establish contractive multi-step MPC with and without
reoptimization and compare it to classic MPC. The idea behind these approaches
is to use the fs-CLF as running cost. These new design approaches are
particularly relevant in situations where information exchange between plant
and controller cannot be ensured at all time instants. An example shows the
different behavior of the proposed controller design approaches.
