Event-Triggered <italic>L</italic>₂&#x2212;<italic>L</italic>_&#x221E; Exponential Consensus of Leader-Follower Multi-Agent Systems

Abstract

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.

Keywords

• Leader-follower
• multi-agent systems
• event-triggered
• L₂−L∞
• exponential consensus