New stabilizability conditions for discrete-time linear parameter varying systems

New stabilizability conditions for input-saturated multi-model Linear Parameter Varying (LPV) discrete-time systems are proposed. They are obtained by means of a "refinement" of the usual quadratic stabilizability conditions. It is proven that such conditions can be made significantly more tight by a better characterization of the politopic set which embeds the true LPV parameter realization. An application to a computationally low demanding "off-line" Receding Horizon Control (RHC) scheme is provided. A numerical example is also presented in order to show that the regulation strategy based on the refined conditions significantly improves the performance of the control strategy and its basin of attraction.