Finite-Time Pinning Event-Triggered Control for Bipartite Consensus of Hybrid-Order Heterogeneous Multi-Agent Systems with Antagonistic Links

Finite-time consensus problem of hybrid-order heterogeneous multi-agent systems under a signed digraph topology is investigated in this paper. For heterogeneous multi-agent systems composed of first-order and second-order agents, a novel pinning event-triggered control protocol is devised to facilitate the attainment of the desired consensus state within a finite time. This control method overcomes communication barriers between first-order and second-order multi-agent systems, achieving effective control performance while reducing controller update frequency and communication costs. Based on graph theory and the Lyapunov stability method, several novel matrices are defined to address the finite-time consensus problem in hybrid-order multi-agent systems, and these matrices also facilitate the theoretical derivation process. Furthermore, it is demonstrated that the control protocol designed for hybrid-order systems is devoid of Zeno behavior. Finally, a detailed numerical example is supplied to illustrate the validity of the theoretical analysis.