Distributed Nonrecursive Averaging Filters for Quantized Consensus: An Edge Sensitivity Design Approach

This article studies the distributed nonrecursive averaging filter design for the quantized consensus of discrete-time first-order multiagent systems over undirected and connected networks. The quantized consensus problem is cast into the robust consensus problem with sector bound uncertainties associated with the edges of communication graphs, and then an edge sensitivity design approach is utilized for the filter parameter design. Necessary and sufficient conditions for the filter parameter for preserving robust consensus with sector bound uncertainties are provided, which are shown to be dependent on the $\mathcal {H}_{\infty }$ norm of the edge complementary sensitivity transfer matrix of the closed-loop multiagent system. Then, the optimal filter parameter design is provided by solving a constrained optimization problem, under which robust consensus with maximal allowable sector bound parameter is reached. The results show that the supremum of the sector bound parameter of the logarithmic quantizer for preserving robust consensus is independent of the communication network topologies and the sampling period.