This　paper　addresses　the　robust　performance　synthesis　problem　for　systems　with　positive-real　or　negative-imaginary　uncertainty.　The　conventional　robust　performance　design　methods　are　mostly　based　on　the　gain　information　of　uncertainty,　which　is　not　suitable　for　uncertainties　characterized　by　the　phase　information.　The　approach　taken　here　is　based　on　the　input-output　relation　of　systems　in　the　frequency　domain,　which　enables　a　less　conservative　yet　numerically　tractable　solution　to　the　robust　performance　synthesis.　The　effectiveness　is　validated　through　a　detailed　case　study　on　the　head　positioning　control　of　hard　disk　drives.　The　results　and　comparison　demonstrate　that　the　proposed　method　can　achieve　a　much　higher　robust　performance　than　existing　methods.　(C)　2017　Elsevier　Ltd.　All　rights　reserved.