Designing Distributed Specified-Time Consensus Protocols for Linear Multiagent Systems Over Directed Graphs

This technical note addresses the distributed specified-time consensus protocol design problem for multiagent systems with general linear dynamics over directed graphs. By using motion planning approaches, a novel class of distributed consensus protocols are developed. With a prespecified settling time, the proposed protocols solve the consensus problem of linear multiagent systems over directed graphs containing a directed spanning tree. In particular, the settling time can be offline prespecified, according to task requirements. Compared with the existing results for multiagent systems, to our best knowledge, this is the first time specified-time consensus problems are raised and solved for general linear multiagent systems over directed graphs. Extensions to the specified-time formation flying are further studied for multiple satellites described by Hill equations.