This paper deals with the asymptotic tracking of periodic trajectories for hybrid systems having linear dynamics in each operating mode and isolated discrete switching events (switching systems). Parametric uncertainties are considered and the dimension of the state vector is allowed to vary among modes. To deal with the hybrid nature of the system, and the possible discontinuities of its solutions at switching times, a properly amended tracking control problem is defined and a feedback control law based on a discontinuous version of the classical internal model principle is proposed. The innovative design of the discrete-time dynamics of the compensator guarantees the robust existence of a steady-state response giving zero tracking error in the controlled output, and local convergence to it.