The purpose of this note is to consider the quadratic stabilization of LPV systems in the realistic case where only Gaussian noisy parameter measures are available. Though neglected in the actual literature on LPV systems, this question is particular important because in all situations of a practical interest the parameter measurements (or estimates) are never exact. The assumed noisy nature of physical parameter readings requires a specifically developed approach consisting of mixed robust and LPV control methods. In the present case, an approach based on a vertex result on interval time varying (ITV) matrices is proposed. This allows the solvability conditions to be stated in terms of a set of LMI's, whose number is independent of the number of time-varying parameters.