Singularly perturbed filters for dynamic average consensus

This paper proposes two continuous-time dynamic average consensus filters for networks described by balanced and weakly-connected directed topologies. Our distributed filters, termed 1st-Order-Input (FOI-DCF ) and 2nd-OrderInput Dynamic (SOI-DCF ) Consensus Filters, respectively, allow agents to track the average of their dynamic inputs within an O(ǫ)-neighborhood. The convergence results and stability analysis rely on singular perturbation theory for nonautonomous systems. The only requirement on the set of reference inputs involves continuous bounded derivatives, up to the second derivative for FOI-DCF and up to the third derivative for SOI-DCF . For the special case of dynamic inputs offset by a static value, we show that SOI-DCF converges to the exact dynamic average with no steady-state error. Numerical examples show how the proposed algorithms closely track the average of dynamic inputs.