Bipartite consensus of multi-agent systems with randomly varying nonlinearities via uncertain pinning control under directed signed switching topologies

This paper investigates the bipartite consensus problem for multi-agent systems via uncertain pinning control under directed signed switching topologies. The agent dynamics incorporate randomly varying nonlinearities and parameter uncertainties to reflect more realistic environmental influences. To handle the uncertain connectivity between the leader and followers induced by switching topology, a distributed pinning control protocol is developed. The main contributions are summarized in two theorems. A suitable multiple Lyapunov function is constructed, and M -matrix theory is employed for multi-agent systems without and with time-varying delays. Sufficient conditions for achieving bipartite consensus are established in the form of linear matrix inequalities (LMIs). These conditions ensure that all followers converge asymptotically to either the leader’s state or its opposite. The convergence direction depends on their subgroup affiliation. Finally, the effectiveness of the proposed control strategy is demonstrated through theoretical analysis and supported by numerical simulations.