The robust ripple-free asymptotic tracking and disturbance rejection problem is studied for sampled-data systems whose matrices are assumed to depend on some "physical" parameters, each of which possibly affects all the elements of the matrices describing the system, and for the case when only a subset of the scalar outputs must track corresponding exogenous reference signals; ripple-free dead-beat regulation and tracking is also required at the nominal parameters. The necessary and sufficient conditions are given for the existence of a solution which may exist even vi hen no solution exists for wholly independent variations of the entries of the matrices describing the system. A design procedure of both the continuous-time internal model and the discrete-time controller is also outlined.