  Polyhedral control Lyapunov functions (PCLFs) are exploited in finite-horizon
linear model predictive control formulations in order to guarantee the maximal
domain of attraction (DoA), in contrast to traditional formulations based on
quadratic control Lyapunov functions. In particular, the terminal region is
chosen as the largest DoA, namely the entire controllable set, which is
parametrized by a level set of a suitable PCLF. Closed-loop stability of the
origin is guaranteed either by using an "inflated" PCLF as terminal cost or by
adding a contraction constraint for the PCLF evaluated at the current state.
Two variants of the formulation based on the inflated PCLF terminal cost are
also presented. In all proposed formulations, the guaranteed DoA is always the
entire controllable set, independently of the chosen finite horizon.
Closed-loop inherent robustness with respect to arbitrary, sufficiently small
perturbations is also established. Moreover, all proposed schemes can be
formulated as Quadratic Programming problems. Numerical examples show the main
benefits and achievements of the proposed formulations.
