Distributed PD Control for the Exponential Signed Average Consensus by using Artificial Delays

This paper deals with the exponential average consensus problem for cooperative/antagonistic Multi-Agent Systems (MASs) sharing information over signed networks. To solve the problem, we present a novel distributed Proportional-Derivative (PD) control, where, by exploiting the artificial delay approach, the derivative action is approximated via the finite-difference method. This leads to a distributed Proportional-Derivative Retarded (PDR) controller with a small enough sampling period t > 0. By means of the Lyapunov-Krasovskii functional and the Halanay lemma, the exponential stability of the resulting delayed closed-loop network is ensured. The theoretical analysis also allows establishing a suitable tuning rule for the proportional and derivative gains w.r.t. the delay margin and communication network features. Simulation results confirm the effectiveness of the proposed PDR in ensuring the bipartite average consensus and proves its flexibility in also guaranteeing the average consensus over unsigned graphs.