Event-Triggered L2−L∞ Exponential Consensus of Leader-Follower Multi-Agent Systems

This paper investigates the
$\mathcal {L}_{2}-\mathcal {L}_{\infty }$
exponential consensus control problem of leader-follower multi-agent systems based on an event-triggered strategy. It begins by establishing an error system and provides a sufficient condition guaranteeing exponential stability of the error system while satisfying the
$\mathcal {L}_{2}-\mathcal {L}_{\infty }$
performance index. Subsequently, utilizing the condition, a design method for the
$\mathcal {L}_{2}-\mathcal {L}_{\infty }$
controller is presented. Finally, through a numerical example, this paper discusses the relationship between optimal
$\mathcal {L}_{2}-\mathcal {L}_{\infty }$
performance index and the maximum sampling period under different topological structures. The effectiveness of the proposed theoretical framework is validated through the numerical example.