Robust consensus of higher order agents over cycle graphs

This paper considers identical agents modeled as higher order linear systems whose dynamics are not precisely known and obtains conditions for consensus of a system of such imprecisely modeled identical linear systems. The state information is exchanged between the agents over a cycle graph. The imprecision in the models of the agents, represented by gain margins of certain transfer functions, is directly related to the parameters of the cycle digraph and it is shown that the number of agents can play a significant role in ensuring consensus among the agents. Additionally, perturbations are also considered in the edge weights of the cycle graph and the tolerable limits on such perturbations are derived. Thus, combined effects of these two forms of uncertainties/perturbations are investigated in this work. Simulations support the theoretical results.