Somenewlinearmatrixinequality(LMI)representationsfordeley-independentanddelay-dependentstabilityconditionsareobtainedbyintroducingadditionalmatricesandeliminatingtheproductcouplingofthesystemmatricesandtheLyapunovmatrices.Theresultsimproveconservativenessofthegivenconditionsfortheanalysisandthedesignoftime-delaysystemswithpolytopic-typeuncertainty.