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This paper presents a stabilizing tube-based MPC synthesis for LPV systems.We employ terminal constraint sets which are required to be controlledperiodically contractive. Periodically (or finite-step) contractive sets areeasier to compute and can be of lower complexity than "true" contractive ones,lowering the required computational effort both off-line and on-line. Undercertain assumptions on the tube parameterization, recursive feasibility of thescheme is proven. Subsequently, asymptotic stability of the origin isguaranteed through the construction of a suitable terminal cost based on anovel Lyapunov-like metric for compact convex sets containing the origin. Aperiodic variant on the well-known homothetic tube parameterization thatsatisfies the necessary assumptions and yields a tractable LPV MPC algorithm isderived. The resulting MPC algorithm requires the on-line solution of a singlelinear program with linear complexity in the prediction horizon. The propertiesof the approach are demonstrated by a numerical example.

Stabilizing Tube-Based Model Predictive Control: Terminal Set and Cost Construction for LPV Systems (extended version)