ThispaperconsidersH-infinitycontrolproblemforintervaldescriptorsystems.NecessaryandsufficientLMI-basedconditionsarederivedforquadratic-likeH-infinitycontrolanalysisofintervaldescriptorsystems.Usingtheanalysisresult,twotypesoffeedbackcontrollersaredesignedsothattheclosed-loopintervaldescriptorsystemsareadmissiblewithH-infinity-normlessthanaprescribedvalue.Tothebestoftheauthors’sknowledge,thisisthefirstpapertodealwiththeH-infinitycontrolproblemofintervaldescriptorsystemsintheliterature.