Abstract: Becauseofthecouplingeffectbetweentheangularvelocitiesofeachaxis,thenonlineardynamicsofthesatellitemustbeconsideredforthecontroloflargeattitudemaneuvers.Besides,thekinematicsdifferentialequationoftheattituderepresentationisalsononlinear.Thesumofsquares(SOS)approachwasproposedasasynthesismethodforthenonlinearcontrolsystemdesign.ItisshownthatthefinalresultoftheSOSdesignhasclearphysicalmeanings,thoughitisanumericalmethod.Infact,theresultingcontrollawcanbeviewedasanonlinearversionofthePDcontrol.ToavoidthepeakvalueofthecontrolinputcausedbytheintrinsicpropertiesoftheMRPs,asaturationdesignwasproposed.Theconvergenceofthetimeresponseundersaturationcanbeprovedbythepassivitynatureofthesystem.AdiagonaldominanceprocedurewasalsoproposedtoreducethenumericalerrorsoftheSOSapproach.TheproposedSOSmethodcanbeusedtosolveanalyticallyunsolvablenonlinearproblemsandwouldhaveawideareaofapplicationsinthenearfuture.

Key words: Sumofsquares, Nonlinearcontrol, Controlsynthesis, Attitudecontrol