In this paper, the consensus problem for higher-order descriptor multi-agent systems (DMASs) with time-delays is investigated. Firstly, a distributed consensus protocol based on output feedback is proposed. Secondly, the state transformation is presented to convert the consensus problem into the stability problem. Based on the Lyapunov theory and the linear matrix inequality (LMI) method, sufficient conditions in terms of LMIs are derived to ensure that consensus of DMASs can be achieved. Moreover, the consensus problem for higher-order DMASs with delays is solved under two cases where interaction topologies are undirected and directed, which is more complicated and challenging. Finally, numerical simulations are provided to demonstrate the effectiveness of our results.

中文翻译：

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具有通信时延的高阶描述符多代理系统的共识条件

在本文中，研究了具有时间延迟的高阶描述符多代理系统（DMAS）的一致性问题。首先，提出了一种基于输出反馈的分布式共识协议。其次，提出状态转换，将共识问题转化为稳定性问题。基于李雅普诺夫理论和线性矩阵不等式（LMI）方法，推导出了LMI方面的充分条件，以确保可以实现DMAS的一致性。此外，具有延迟的高阶 DMAS 的共识问题在交互拓扑为无向和有向两种情况下得到解决，这更加复杂和具有挑战性。最后，提供了数值模拟来证明我们结果的有效性。