This paper addresses L-2-gain analysis and robust H-infinity control of nonlinear sampled-data systems described by a polynomial linear parameter varying (PLPV) model. First, conditions for L-2-gain analysis of sampleddata PLPV systems are derived using a modified Krasovskii functional in which the distance between the real and measured parameters are considered as uncertainties. The resulting conditions are formulated in terms of parameterised linear matrix inequalities (PLMI). Second, a solution approach for satisfying PLMI conditions over the set of whole parameters and uncertainties is proposed using the sum-of-squares decomposition method. Third, conditions for robust H-infinity sampled-data controller synthesis for nonlinear systems described by PLPV models are derived in terms of parameterised bilinear matrix inequalities (PBMI) with the maximum allowable sampling period as the parameter. To make the resulting bilinear matrix inequality (BMI) problems tractable, an iterative algorithm is developed and utilised to solve the problem. Finally, the effectiveness of the proposed approach is verified using several real-world examples.