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Lag‐bipartite consensus of linear multiagent systems under saturating input over signed graph

The objective of this study is to investigate lag-bipartite consensus of linear multiagent systems under saturating input with dead-zone constraint where two separate groups of follower agents reach the modulus of the leader state, but of opposite sign with a certain delay. The leader-follower bipartite consensus problem of saturating input with dead-zone is considered with the input signals of the followers being subjected to leader-influenced input additive uncertainties and disturbances. It is shown that if the agents interacting with each-other over the structurally balanced undirected graph having a directed spanning tree rooted at the leader are asymptotically null controllable with bounded controls, then the two proposed control laws - (i) a low-high gain based control law and (ii) a low-gain based variable-structure continuous tracking control law, can achieve lag-bipartite consensus as long as the initial conditions of all the agents remain within a priori bounded set. The numerical simulations establish the effectiveness of the theoretical results.