The　authors　of　this　paper　design　an　optimal　and　a　subopimal　H∞　controller　with　states　feedback　based　on　H∞　disturbance　attenuation　and　linear　matrix　inequalities.　Designing　this　controllers　needn＇t　deal　with　seismic　signal.　This　method　takes　little　time　online　and　calculates　directly　and　simply.　Furthermore,　the　authors　analyse　the　influence　of　evaluation　signal　on　seismic　excitation　attenuation.　Finally,　an　example　is　given　in　this　paper.　The　results　of　numerical　analysis　and　comparion　demonstrate　that　these　controllers　can　restrain　the　seismic　excitations.