Multiplex PI-Control for Consensus in Networks of Heterogeneous Linear Agents

In this paper, we propose a multiplex proportional-integral approach, for solving consensus problems in networks of heterogeneous nodes dynamics affected by constant disturbances. The proportional and integral actions are deployed on two different layers across the network, each with its own topology. Furthermore, the contribution of the network topology and node dynamics have been systematically separated giving some sufficient conditions guaranteeing convergence. The effectiveness of the theoretical results is illustrated using a power network model.