The　paper　uses　an　LMI-based　iterative　nonlinear　optimization　algorithm　to　establish　a　method　of　designing　state-feedback　controllers　for　power　systems　with　a　time-varying　delay.　This　method　is　based　on　the　delay-dependent　stabilization　conditions　obtained　by　free　weighting　matrix　approach.　In　the　stabilization　conditions,　the　upper　bound　of　wide-area　signal＇s　transmission　delays　is　taken　into　consideration.　Combining　theories　of　state　observer,　the　adeptive　supervisory　controller　(ASC)　is　designed　and　time-delay　output　feedback　robust　controller　is　realized　for　power　system.　The　ASC　uses　the　input　information　from　wide-area　measurement　systems　(WAMS)　and　dispatches　supplementary　control　signals　to　the　available　local　controllers.　Simulation　study　in　the　New　England　test　power　system　confirm　that　the　proposed　ASCs　can　dampen　power　oscillation　effectively　and　is　robust　to　time-varying　delay　condition.