Consensus of autonomous agents is a benchmark problem in cooperative control. In this paper, we consider standard continuous-time averaging consensus policies (or Laplacian flows) over time-varying graphs and focus on robustness of consensus against communication delays. Such a robustness has been proved under the assumption of uniform quasi-strong connectivity of the graph. It is known, however, that the uniform connectivity is not necessary for consensus. For instance, in the case of undirected graph and undelayed communication consensus requires a much weaker condition of integral connectivity. In this paper, we show that the latter results remain valid in presence of unknown but bounded communication delays, furthermore, the condition of undirected graph can be substantially relaxed and replaced by the conditions of non-instantaneous type-symmetry. Furthermore, consensus can be proved for any feasible solution of the delay differential inequalities associated to the consensus algorithm. Such inequalities naturally arise in problems of containment control, distributed optimization and models of social dynamics.

中文翻译：

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共识算法延迟鲁棒性的新结果

自治代理的共识是合作控制中的一个基准问题。在本文中，我们考虑了时变图上的标准连续时间平均共识策略（或拉普拉斯流），并关注共识对通信延迟的鲁棒性。这种鲁棒性已经在图的均匀准强连通性假设下得到证明。然而，众所周知，统一连接对于达成共识并不是必需的。例如，在无向图和无延迟通信共识的情况下，需要弱得多的积分连接条件。在本文中，我们证明了后者的结果在存在未知但有界的通信延迟的情况下仍然有效，此外，无向图的条件可以大幅度放宽，代之以非瞬时类型对称的条件。此外，对于与共识算法相关的延迟微分不等式的任何可行解，都可以证明共识。这种不平等自然会出现在遏制控制、分布式优化和社会动态模型的问题中。