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Consensus of second-order sampled multi-agent system with delays

This paper studies the consensus problem of second-order multi-agent system with communication delay under fixed topology. First, by the iterative product method, the continuous-time multi-agent system is equivalently transformed into a linear discrete-time system. Then, by algebraic graph theory and matrix theory, we analyze the convergence of the system matrix. Finally, an example is provided to illustrate the effectiveness of the theoretical results. We not only prove the existence of the parameter, sampling period and delays, but also give the approach of how to choose them. In our study, the eigenvalues of the corresponding Laplacian matrix play a key role in reaching consensus.