This　paper　considers　the　problem　of　robust　control　synthesis　such　that　time-delay　multi-agent　systems　are　consensus　and　capture　the　finite　frequency　domain　performance.　Using　a　linear　transformation,　the　consensus　problem　is　first　transformed　into　a　partial　stability　problem.　Then,　based　on　a　dual　version　of　generalised　Kalman-Yakubovich-Popov　(GKYP)　lemma　and　a　partial　multiplier　expansion　method,　new　sufficient　conditions　guaranteeing　the　existence　of　static　output　feedback　controller　are　proposed　in　terms　of　linear　matrix　inequalities　(LMIs)　without　introducing　conservatism.　Finally,　the　effectiveness　of　the　presented　method　is　illustrated　via　a　two-cart-one-spring　system　and　a　numerical　example.