Consensus and synchronization of complex networks via proportional-integral coupling

In this paper we investigate the use of distributed PI actions to achieve consensus and synchronization in complex networks. We show that by extending the classical linear diffusive coupling with an integral action it is possible to achieve better performance and steady-state behavior than with more traditional strategies. After briefly summarizing the theoretical results, we investigate the viability of the proposed strategy via numerical simulations including a representative example inspired from power system models recently presented in the literature.