Adaptive Lag-Bipartite Consensus of Linear Multiagent Systems with a Non-autonomous Leader over Signed Graph

The objective of this paper is to investigate lag-bipartite consensus of linear multiagent systems (MAS) with a non-autonomous leader. The principle focus of this work is to study the collective behaviour of MAS over a signed graph called lag-bipartite consensus in which a group of follower agents tracks the leader trajectory with a certain time-delay, and the other group tracks the opposite of the leader trajectory with the same amount of time-delay. The study is carried out under both static and adaptive couplings. Static coupling uses global information while adaptive coupling uses only relative information between agents and system parameters. It is shown that if the communication topology is connected, then with the design of suitable distributed state-feedback controllers based on static and adaptive coupling gains, and feedback gain matrices, lag-bipartite consensus among the followers and the leader is achieved. The theoretical developments are verified with the numerical simulation results.