A Combined Global and Local Identification Approach for LPV Systems**This research is sponsored by the Fund for Scientific Research (FWOVlaanderen) through project G.0002.11, by the KU Leuven-BOF PFV/10/002 Center-of-Excellence Optimization in Engineering (OPTEC), and by the Belgian Program on Interuniversity Poles of Attraction, initiated by the Belgian State, Prime Ministers Office, Science Policy programming (IAP VII, DYSCO). Goele Pipeleers is a Postdoctoral Fellow of the Research Foundation-Flanders (FWO - Vlaanderen).