This paper deals with the problem of consensus in multi-agent systems. The consensus is investigated considering directed networks composed by identical agents described by linear models of arbitrary order, subject to input saturation and non-uniform time-varying delays. The main results are sufficient conditions for consensus analysis and design of distributed consensus protocols for multi-agent systems. In addition, because the saturation might prevent the multi-agent system to attain consensus on some set of initial conditions, it is also proposed a strategy to calculate a region in which the consensus is guaranteed. The results follow from the Lyapunov–Krasovskii theory and are formulated in the linear matrix inequalities (LMIs) framework. Finally, we present examples to illustrate the effectiveness of the proposed method in contrast with similar approaches existing in the literature.

本文讨论了多智能体系统中的共识问题。在考虑输入饱和和非均匀时变时延的情况下，考虑由相同代理组成的有向网络来研究共识，该代理由任意阶线性模型描述。主要结果是为进行多主体系统的共识分析和分布式共识协议设计提供了充分的条件。另外，由于饱和度可能会阻止多主体系统在某些初始条件上达成共识，因此，还提出了一种计算可确保达成共识的区域的策略。结果来自Lyapunov–Krasovskii理论，并以线性矩阵不等式（LMI）框架表示。最后，