Under　the　background　of　energy　interconnection　and　low-carbon　electricity,　integrated　energy　systems　(IES)　play　an　important　role　in　energy　conservation　and　emission　reduction.　To　further　promote　the　low-carbon　transition　of　energy,　this　paper　proposes　a　distributed　robust　optimal　control　strategy　for　IESs　based　on　energy　trading.　Firstly,　an　IES　model　that　includes　an　electric　hydrogen　module　and　gas　hydrogen　doping　combined　heat　and　power　is　established,　and　ladder-type　carbon　trading　is　introduced　to　reduce　carbon　emissions.　Secondly,　for　the　energy　trading　issues　between　photovoltaic　(PV)　prosumers　and　IES,　a　bi-level　model　is　constructed　using　Stackelberg　game　method,　where　the　IES　acts　as　the　leader　and　the　PV　prosumers　as　the　followers.　Noteworthy,　a　distributed　robust　optimization　method　is　used　to　address　the　uncertainty　of　renewable　energy　and　load.　Additionally,　the　Nash　bargaining　method　ensures　an　equitable　balance　of　benefits　among　the　various　IESs　and　encourages　them　to　participate　in　market　transactions.　On　this　basis,　an　intermediary　transaction　mode　is　proposed　to　address　cheating　behaviors　in　trading.　Finally,　the　simulation　results　demonstrate　that　the　proposed　strategy　not　only　effectively　promotes　cooperative　operation　among　multiple　IESs　but　also　significantly　reduces　the　system＇s　operating　costs　and　carbon　emissions.