Distributed consensus protocol design for general linear multi‐agent systems: a consensus region approach

This study presents a consensus region approach to designing distributed consensus protocols for multi‐agent systems with general continuous‐time linear node dynamics. The consensus region approach has a favourable decoupling feature, which decouples the design of the feedback gain matrices of the consensus protocols from the communication graph. Multi‐step algorithms are presented to construct the fixed‐gain consensus protocols, which requires the smallest non‐zero eigenvalue of the Laplacian matrix. To remove this limitation, distributed adaptive protocols with time‐varying coupling weights are designed for the cases with undirected and directed graphs, which can be implemented in a fully distributed fashion. The robustness issue of the adaptive protocols in the presence of external disturbances is also discussed. For the case where there exists a leader of bounded unknown control input, distributed discontinuous and continuous controllers are designed to solve the distributed tracking problem.