On topology and dynamics of consensus among linear high-order agents

Consensus of a group of agents in a multi-agent system with and without a leader is considered. All agents are modelled by identical linear n-th order dynamical systems while the leader, when it exists, may evolve according to a different linear model of the same order. The interconnection topology between the agents is modelled as a directed weighted graph. We provide answers to the questions of whether the group converges to consensus and what consensus value the group eventually reaches. To that end, we give a detailed analysis of relevant algebraic properties of the graph Laplacian. Furthermore, we propose an LMI-based design for group consensus in the general case.