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This paper revisits the problem of multi-agent consensus from a graph signalprocessing perspective. By defining the graph filter from the consensusprotocol, we establish the direct relation between average consensus ofmulti-agent systems and filtering of graph signals. This relation not onlyprovides new insights of the average consensus, it also turns out to be apowerful tool to design effective consensus protocols for uncertain networks,which is difficult to deal with by existing time-domain methods. In this paper,we consider two cases, one is uncertain networks modeled by an estimatedLaplacian matrix and a fixed eigenvalue bound, the other is connected graphswith unknown topology. The consensus protocols are designed for both casesbased on the protocol filter. Several numerical examples are given todemonstrate the effectiveness of our methods.

New results on multi-agent system consensus: A graph signal processing perspective