Consensus in networks with arbitrary time invariant linear agents

In this paper, we study the consensus problem from a general control theoretical perspective. For that we identify three entities: the multiagents network that constitutes the control plant, consensus as a control objective, and the consensus algorithm as a feedback controller for the network. Consensus is redefined through the idea of organization (a linear transformation) to define an error vector that resumes the characteristics of the network. With this formulation, we can translate the general consensus problem into a stability problem and, from there, use classical Control Theory to analyze the case of agents with arbitrary linear time invariant dynamics (and not only integrator dynamics) and Laplacian algorithms. The paper is complemented with numeric examples to illustrate the proposed analysis methodology.