This paper presents an application of polynomial linear parameter varying (LPV) methods based on matrix sum-of-squares (SOS) relaxations for the end-effector position controller analysis of flexible-link manipulators. The proposed approach exploits an effective way for solving polynomial parameter-dependent linear matrix inequalities (PD-LMIs) and allows to consider more general admissible sets than hyper-rectangles or convex polytopes. This leads to less conservative results when considering an H_∞ output feedback controlled system. In particular, some performance analysis results are presented. A practical case study shows the effectiveness of the proposed methodology.