  This paper presents a stabilizing tube-based MPC synthesis for LPV systems.
We employ terminal constraint sets which are required to be controlled
periodically contractive. Periodically (or finite-step) contractive sets are
easier to compute and can be of lower complexity than "true" contractive ones,
lowering the required computational effort both off-line and on-line. Under
certain assumptions on the tube parameterization, recursive feasibility of the
scheme is proven. Subsequently, asymptotic stability of the origin is
guaranteed through the construction of a suitable terminal cost based on a
novel Lyapunov-like metric for compact convex sets containing the origin. A
periodic variant on the well-known homothetic tube parameterization that
satisfies the necessary assumptions and yields a tractable LPV MPC algorithm is
derived. The resulting MPC algorithm requires the on-line solution of a single
linear program with linear complexity in the prediction horizon. The properties
of the approach are demonstrated by a numerical example.
