Consensus tracking of linear multi-agent systems under a networked detectability condition with reduced-order protocols

This study addresses the consensus tracking problem of linear multi-agent systems under a networked detectability condition with reduced-order protocols. The communication subgraph among followers is undirected and connected. It is assumed that only partial relative state information of the leader can be obtained by each follower. The networked detectability condition only requires that the leader is jointly detectable to all followers, without any detectability requirement on an individual follower. Under the assumption that the system is neurally stable, distributed observer-type consensus protocols are constructed for both continuous- and discrete-time linear multi-agent systems. By using tools from matrix theory and linear system analysis, some sufficient conditions are derived to reach consensus tracking. One favourable feature of this study is that the traditional detectability condition for an individual system is extended to the networked case and in contrast to the relevant available results, reduced-order observers are presented to reduce information redundancy. Simulation examples are given to illustrate the theoretical results.