Robust Consensus With Edge-Based Multiplicative Uncertainties via Recursive Channel Filters

This brief considers the robust consensus issue subject to channel uncertainties by adopting the first-order channel recursive filters for continuous- as well as discrete-time multi-agent systems (MASs). The considered uncertainties are edge-based multiplicative ones that are bounded in $\mathcal {H}_{\infty }$ norm. The edge sensitivity function matrix (ESFM) and the edge complementary sensitivity function matrix (ECSFM) are defined for the continuous- and discrete-time MASs. Then, an edge sensitivity scheme is used for seeking the filter parameters, by which we show that the consensusability margins of MASs are associated with the edge complementary sensitivity function matrices of the MASs. The parameter conditions for the recursive filters are also be provided, under which the robust consensus with multiplicative uncertainties is achieved with maximal consensusability margins.