Second- and Third-Order Stability Bounds for High-Order Linear Consensus on Directed Graph Topologies with Partial Relative State Information and Global/Local Gains

A general high-order linear consensus protocol is proposed for coupling topologies defined by directed graphs with partial relative state information and a reference model with lobal/local gains. Necessary and sufficient second-order stability bounds for the cases of relative position feedback with reference velocity and relative position and velocity feedback are then reviewed. Next, new necessary and sufficient stability bounds are obtained for third-order consensus for three cases of feedback of full and partial relative state information. The stability bounds obtained, unlike in prior studies, allow for the gains to be conveniently selected in a sequential manner and are shown to utilize those for second-order consensus. Comparisons with conservative stability bounds from previous studies are shown, and illustrative examples of the proposed consensus protocols and the obtained stability bounds are provided.