This paper considers the problem of designing a state-feedback control law which "minimizes" multiple quadratic performance objectives in the presence of uncertain linear plant dynamics. Vector optimization techniques are used to minimize upper-bounds on each performance objective (guaranteed-cost). By exploiting the linear uncertainty bound introduced by Bernstein (1987), the vector optimization problem is scalarized and Pareto optimal solutions are computed. The theory is applied to a numerical example with two quadratic performance measures.