The problem of state-feedback control design for continuous-time uncertain linear systems is investigated in this paper using a Cartesian product of simplexes, called multi-simplex, to represent the system uncertainties. In this representation, time-invariant, arbitrarily time-varying and bounded time-varying parameters can be treated simultaneously in an appropriate way. As the main novelty, the method allows to synthesize control gains depending only on some parameters selected by the designer. The usefulness of such flexibility is illustrated through numerical experiments, including the control design of a helicopter model borrowed from the literature. The solutions are based on parameter-dependent Lyapunov functions and LMI relaxations of increasing precision.