Distributed Consensus of Linear Multiagent Systems: Laplacian Spectra-Based Method

The consensusability problems of general linear multiagent systems considering directed topologies are explored from a frequency domain perspective in this paper. By investigating the properties of Laplacian spectra, a consensus criterion is established based on the stability of several complex weighted closed-loop systems. Furthermore, for single-input multiagent systems, frequency domain consensusability criteria are proposed on the basis of the stability margins, which depend on the H ∞ norm of the complementary sensitivity function determined by the agents' unstable poles. The corresponding design procedure is also developed. A numerical example is also presented to validate the proposed consensusability results.