Necessary and sufficient conditions for consensus of third-order discrete-time multi-agent systems in directed networks

This paper studies consensus of third-order discrete-time multi-agent systems in directed networks. When each agent can only receive its neighbor’s position information, necessary and sufficient conditions for consensus of the system are established. Compared with the preceding work, we not only answer what consensus value the system eventually achieves, but also clearly show the equivalent relationship between consensus, scaling parameters and nonzero eigenvalues of the involved Laplacian matrix. Illustrative examples are also given to demonstrate the effectiveness of the obtained theoretical results.