A previous article has investigated the problem of the preservation of the observability under sampling in the framework of compact manifolds. A natural generalization of the cited result would be to extend it to the systems globally Lipschitzian defined on non compact manifolds. A simple representative of this class of systems is constituted by the set of bilinear systems, for this particular class of systems the preservation of the property of observability has been shown in a previous work. In this paper, we deal with the preservation of the observability under sampling for globally Lipschitzian systems defined on $\mathbb{R}^n$