Nonlinear consensus via continuous, sampled, and aperiodic updates

We consider a first-order multi-agent system with nonlinear control protocols performing consensus. We first address the convergence properties of the continuous system. Then periodically sampled control inputs are treated, where we derive explicit upper bounds on the sampling interval to preserve global stability. Moreover, we design an aperiodic and event-triggered updating law to reduce the control efforts even further while ensuring the closed-loop stability and providing a strictly positive lower bound on the inter-execution time. Finally, the robustness of this approach with respect to additive disturbances is examined by applying ℒ2 gain analysis.