Prescribed-time leader-following consensus of linear multi-agent systems by bounded linear time-varying protocols

This paper considers the prescribed-time leader-following consensus problem of input-constrained linear multi-agent systems under generally directed communication topology in two cases: the Laplacian matrix related to the entire communication topology between agents is either known or unknown. In particular, the consensus problem for the former case is solved by a novel bounded linear time-varying (LTV) protocol, where the feedback gain is formulated by the parametric Lyapunov equation and the knowledge of the Laplacian matrix. Moreover, by utilizing a distributed observer, a fully bounded LTV protocol is proposed for the latter case. It should be noted that, compared with the existing results, the system under consideration is more general, the designed protocols are linear, and the consensus problem is accomplished even in a fully distributed manner. Finally, the effectiveness of the proposed approach is verified by a numerical example.