ThispaperdiscussesH-infinitystatefeedbackcontrolforanetworkedcontrolsystemwithtime-varyingdelays.Basedonthefree-weighingmatrixmethod,adelay-dependentstabilitycriterionsatisfyingaprescribedH-infinitynormboundispresentedforanNCSwithunknown,time-varyingandboundeddelays.Andthen,thecriterionistransformedintosufficientconditionsbasedonlinearmatrixinequalitiesforH-infinitycontrol.TheconditionsthusobtainedarealsousedtodesignanH-infinitystatefeedbackcontroller.ThisdesignmethodisfurtherextendedtosolvethedesignproblemofrobustH-infinitystatefeedbackcontrol.Anumericalexampledemonstratesthevalidityofthemethod.