Most　of　the　recent　results　on　the　leader-following　rendezvous　problem　focus　only　on　the　deterministic　multi-agent　systems　without　external　disturbances　and　plant　uncertainties.　In　this　paper,　we　will　present　a　novel　distributed　internal　model　approach　to　further　study　the　leader-following　rendezvous　problem　for　double-integrator　multi-agent　systems　subject　to　both　external　disturbances　and　plant　uncertainties.　We　provide　both　the　distributed　full　state　feedback　control　and　the　distributed　partial　state　feedback　control　without　velocity　measurement.　In　both　control　schemes,　we　will　give　the　suitable　distributed　internal　model　to　convert　the　rendezvous　problem　into　the　stabilization　problem　with　connectivity　preserving　for　their　augmented　systems.　We　stabilize　the　corresponding　augmented　systems　by　the　high　gain　feedback　control　based　on　a　new　potential　function.　Comparing　with　some　recent　results,　our　design　can　handle　a　large　class　of　reference　signals,　external　disturbances,　and　plant　uncertainties.　(C)　2015　Elsevier　Ltd.　All　rights　reserved.