This　work　presents　a　consensus　strategy　for　multiagent　networked　systems　with　time-varying　delays.　A　new　control　technique　is　first　developed,　named　observer-based　distributed　periodic　event-triggered　control.　Aiming　at　leader-following　consensus　strategy,　the　state　update　of　every　follower　agent　just　demands　the　neighbor　state　at　the　moment　of　its　own　event.　Then,　based　on　matrix　inequalities,　the　sufficient　criteria　for　the　systems　under　consideration　are　established,　which　is　easier　to　satisfy　and　shows　that　the　consensus　can　be　reached　exponentially.　Finally,　one　numerical　example　is　presented　to　indicate　the　performance　of　the　proposed　method.