In　the　upcoming　decades,　connected　vehicles　will　join　regular　vehicles　to　appear　on　roads,　and　the　characteristics　of　traffic　flow　will　he　changed　accordingly.　To　model　the　heterogeneous　traffic　mixing　regular　and　connected　vehicles,　a　generic　car-following　framework　is　first　proposed　in　this　paper.　A　linear　stability　condition　is　theoretically　derived,　which　indicates　that　the　stability　of　the　heterogeneous　traffic　is　closely　related　to　the　penetration　rate　and　the　spatial　distribution　of　connected　vehicles.　The　generic　car-following　framework　is　applied　by　taking　the　Intelligent　Driver　Model　as　an　example,　and　it　is　shown　that　connected　vehicles　can　obviously　enhance　the　stability　of　traffic　flow　and　improve　traffic　efficiency　in　particular　when　traffic　is　in　congestion.　Moreover,　a　driver　assistance　strategy　based　on　distributed　feedback　control　is　developed　for　connected　vehicles,　and　the　simulation　results　show　that　the　proposed　driver　assistance　strategy　performs　satisfactorily　in　stabilizing　traffic　as　well　as　improving　traffic　efficiency.