Orientation and Connectivity Based Criteria for Asymptotic Consensus

In this article, we establish orientation and connectivity based criteria for the agreement algorithm to achieve asymptotic consensus in the context of time-varying topology and communication delays. These criteria unify and extend many earlier convergence results on the agreement algorithm for deterministic and discrete-time multiagent systems.

💡 Research Summary

The paper investigates convergence conditions for the classic agreement (consensus) algorithm in multi‑agent systems where both the communication topology and the transmission delays may vary over time. Each of the N agents holds a scalar state xi(t) and updates it according to

 xi(t + 1) = ∑j=1N Aij(t) · xj(τij(t)),

where A(t)=