A novel energy-based control approach for leader-follower bipartite consensus of heterogeneous multi-agents over antagonistic network interactions

This paper addresses the problem of robust bipartite consensus of heterogeneous linear multi-agent systems (MASs) under external disturbances and antagonistic interactions. The theoretical findings of the bipartite consensus are conducted for both the undirected and directed signed graphs to deal with the cooperative-competitive behavior with neighbor agents. To guarantee the stability and bipartite consensus of heterogeneous dynamics MASs, a dynamic state feedback distributed controller mechanism is established with the aid of Lyapunov criteria, $H_{\infty }$ robust control criteria, and an output regulation approach. A novel $H_{\infty }$ energy-based robustness criterion for the bipartition of heterogeneous MASs to minimize the disturbance effect at output errors has been introduced. This criterion has been imposed on MASs via an objective inequality along with Lyapunov analysis, $L_2$ gain investigation, network characteristics, and norm properties for ensuring the desired robustness objectives. The adequate conditions that ensure the bipartite consensus of heterogeneous MASs are determined as linear matrix inequalities for a simple design investigation. Two numerical examples are demonstrated to check the efficiency of the resultant control schemes.