Event-Based H∞ Consensus of Double-Integrator Multi-Agent Systems: A Prescribed Performance Control Approach

This brief addresses the event-triggered
$H_{\infty }$
consensus problem for double-integrator multi-agent systems with external disturbances under undirected and connected networks. To solve this problem, an edge-based event-triggered nonlinear control protocol is proposed, which is intermittently updated. The proposed protocol guarantees convergence with prescribed transient, steady-state performance and event-based
$H_{\infty }$
consensus. A self-triggered mechanism is further developed to avoid continuous communication among adjacent agents. Based on the above control protocols, we establish a unified prescribed performance control approach which covers finite-time convergence, unknown initial bounds and small overshoot specifications, with specifications achieved by directly replacing the corresponding performance function. The effectiveness of the proposed protocols is ultimately illustrated by a numerical example.