Design Guidelines to Accelerate Consensus Using Intentional Delays in a Multiagent System Over Mixed Graphs

We study a proportional retarded (PR) consensus protocol in a multiagent system with single integrator dynamics where the communication network is described by a mixed graph. As previous work was focused on particular systems that generate real or complex graph Laplacian eigenvalues, the main contribution of this letter is providing analytical PR tuning rules for the general case, where complex and real eigenvalues originate together from the mixed graph. Validations through simulations and experiments in a robotic application are also presented.