The aim of this paper is to investigate the problem of robust stabilization of aperiodic uncertain sampleddata linear systems. Using an impulsive system representation, synthesis conditions are proposed in terms of parameter-dependent linear matrix inequalities (LMIs). Differently from the existing approaches, the resulting state-feedback control gain is not obtained directly from the Lyapunov matrix, easing the task of imposing particular structures to the controller, such as decentralization. Moreover, using a convenient change of variables, a more efficient polynomial approximation is proposed to solve the parameter-dependent LMIs when compared to sum-of-square techniques. An extension to deal with uncertain sampled-data linear systems with periodic sampling interval based on parameter-dependent Lyapunov matrices is also proposed. Numerical examples illustrate the applicability, the advantages, and how the conservativeness of the conditions can be reduced by employing polynomial parameter-dependent decision variables in the proposed conditions when compared with standard approaches from the literature.