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This work explores the edge agreement problem of second-order nonlinearmulti-agent system under quantized measurements. Under the edge agreementframework, we introduce an important concept about the \emph{essential edgeLaplacian} and also obtain a reduced model of the edge agreement dynamics basedon the spanning tree subgraph. The quantized edge agreement problem ofsecond-order nonlinear multi-agent system is studied, in which both uniform andlogarithmic quantizers are considered. We do not only guarantee the stabilityof the proposed quantized control law, but also reveal the explicitmathematical connection of the quantized interval and the convergenceproperties for both uniform and logarithmic quantizers, which has not beenaddressed before. Particularly, for uniform quantizers, we provide the upperbound of the radius of the agreement neighborhood and indicate that the radiusincreases with the quantization interval. While for logarithmic quantizers, theagents converge exponentially to the desired agreement equilibrium. Inaddition, we figure out the relationship of the quantization interval and theconvergence speed and also provide the estimates of the convergence rate.Finally, simulation results are given to verify the theoretical analysis.

Edge Agreement of Multi-agent System with Quantized Measurements via the Directed Edge Laplacian