  This work explores the edge agreement problem of second-order nonlinear
multi-agent system under quantized measurements. Under the edge agreement
framework, we introduce an important concept about the \emph{essential edge
Laplacian} and also obtain a reduced model of the edge agreement dynamics based
on the spanning tree subgraph. The quantized edge agreement problem of
second-order nonlinear multi-agent system is studied, in which both uniform and
logarithmic quantizers are considered. We do not only guarantee the stability
of the proposed quantized control law, but also reveal the explicit
mathematical connection of the quantized interval and the convergence
properties for both uniform and logarithmic quantizers, which has not been
addressed before. Particularly, for uniform quantizers, we provide the upper
bound of the radius of the agreement neighborhood and indicate that the radius
increases with the quantization interval. While for logarithmic quantizers, the
agents converge exponentially to the desired agreement equilibrium. In
addition, we figure out the relationship of the quantization interval and the
convergence speed and also provide the estimates of the convergence rate.
Finally, simulation results are given to verify the theoretical analysis.
