In this article, an internal-model-based event-triggered control is proposed for the rendezvous problem of linear uncertain multi-agent systems. Our approach is not only robust to parametric uncertainty and external disturbances, but also capable of preserving the connectivity of the position-dependent time-varying communication network. The event-triggered mechanism is in a piecewise constant form and thus can be directly implemented in the digital platform. Technically, different from traditional internal model design, a class of distributed dynamic compensators are designed based on sampled relative position and velocity signals to convert the rendezvous problem into a stabilization with connectivity problem of a special augmented system, which is then solved by a piecewise constant stabilizer. Finally, it is proved that the rendezvous problem of the original system is solvable by stabilizing such augmented system and excluding Zeno behavior.