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In this paper, the chaotic lag synchronization of coupled time-delayed systems with two neurons is investigated.We analyze the asymptotic stability for the error dynamical system based on Lyapunov method and linear matrix inequality (LMI) technique. Some new sufficient conditions for determining the lag synchronization between the coupling systems are derived. Above all, we skillfully shift our criterion which is expressed in terms of LMI into the generalized eigenvalue minimization programming (GEVP) for the first time. The minimum of coupling strength is obtained successfully. A numerical experiment illustrates the effectiveness and advantage of our results.