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We propose a method to compute invariant subsets of the region-of-attraction for the asymptotically stable equilibrium points of polynomial dynamical systems with bounded parametric uncertainty. Parameter-independent Lyapunov functions are used to characterize invariant subsets of the robust region-of-attraction. A branch-and-bound type refinement procedure is implemented to reduce the conservatism. We demonstrate the method on a two-state example from the literature and five-state controlled short period aircraft dynamics with and without time delay in the input to the plant.