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This article studies the average-consensus problem of second-order multi-agent sampled control system with time-varying sampling interval. The sampled control protocol is induced from continuous-time linear consensus protocol by using sampling technology and zero-order hold circuit. First, by the iterative method, the continuous-time multi-agent system can be equivalently transformed into a linear discrete-time system. Then, by algebraic graph theory and matrix theory, the authors analyse the convergence of the system and not only prove the existence of the scaling parameter and time-varying sampling interval but also give the approach of how to choose them. In their study, the eigenvalues of the corresponding Laplacian matrix play a key role in reaching consensus. Finally, an example is provided to illustrate the effectiveness of the theoretical results.