This paper proposes a novel discrete-time second-order distributed consensus time synchronization (SO-DCTS) algorithm for wireless sensor networks. The consensus properties and convergence rates of the SO-DCTS algorithm are analyzed for both directed and undirected networks. Additionally, the convergence region and optimal convergence rate of the SO-DCTS algorithm are determined for undirected networks and this convergence rate is shown to be superior to that of the first-order DCTS (FO-DCTS) algorithm under careful algorithm design. Furthermore, the asymptotic expectation and mean square synchronization error are investigated for the SO-DCTS algorithm when there is Gaussian delay between network nodes. Finally, simulation results are provided to verify these analytical results.
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