Fast Consensus of Multi-Agent Systems on Digraphs by Graph Filtering

In this paper, we extend the graph filtering method to the consensus problem on digraphs. By introducing the normalized Laplacian matrix, a time-varying control protocol and the corresponding filter are designed. For the case of known digraphs, a graph filter is designed to reach the finite-time consensus. For the case of unknown digraphs, a periodic control strategy is adopted to achieve consensus asymptotically. By optimizing the worst-case periodic convergence rate, the optimal design of the control sequence is presented to reach fast consensus. Numerical simulations are given to illustrate the effectiveness of our results.