Event-triggered robust bipartite consensus of multi-agent systems under input saturation over directed signed graphs

The goal of developing a consensus protocol for multi-agent systems (MASs) such that the states of all the agents match both in magnitudes and signs is a fundamental challenge in collaborative control theory. Bipartite consensus is an advanced and challenging problem, in which the goal is to devise a controller for two groups of agents so that their states have the same magnitude but opposite signs with respect to their groups. In this work, a robust bipartite consensus approach for higher-order MASs having linear dynamics under input saturation is examined under amplitude-bounded disturbances over a directed signed graph. The approach has been developed via a distributed event-triggered (ET) mechanism, and a condition for attaining robust ET bipartite consensus of MASs using Lyapunov theory and input saturation bound has been investigated. A novel LMI-based robust design that explicitly integrates saturation constraints with distributed ET triggering is proposed, yielding a regional stability characterization and guaranteeing uniformly ultimately bounded bipartite consensus under amplitude-bounded disturbances. The ET approach assures that the Zeno behavior is excluded and provides investigation of a region of stability for the local bipartite consensus under input saturation. Various optimization scenarios of the proposed method for removing sensitivity against initial conditions, for robustness, and for enlarging the control signal are provided. A simulation example is provided to demonstrate the efficacy of the suggested control protocol.