Design of reduced-order distributed controllers for solving the output feedback state consensus problem in a homogeneous multi-agent network is the topic of this paper. The dynamics of each agent in this network is governed by a marginally unstable single-input single-output linear system and each agent can access the relative output of its neighboring agents. Recognizing, possibly for the first time, the similarities between the feedback structures appearing in a well-known low-gain controller design approach for solving the consensus problem and the low-gain approach to the output regulation of stable linear plants, we propose a novel controller design technique for solving the consensus problem. Our technique is frequency-domain based, unlike most of the techniques in the literature which are state–space based. Combining our technique with a recent result on the existence of stable $p^{\mathrm{th}}$-order transfer functions with a desired phase at $p$ given frequencies, we design controllers whose order is significantly lower than the order of the controllers proposed in the consensus literature. The techniques developed in this work can be applied equally to design reduced-order controllers for solving the aforementioned consensus problem in the presence of known, uniform and arbitrarily large communication and input delays in the network.

本文旨在解决均质多主体网络中输出反馈状态共识问题的降阶分布式控制器设计。该网络中每个业务代表的动态受边际不稳定的单输入单输出线性系统控制，每个业务代表可以访问其相邻业务代表的相对输出。我们有可能第一次认识到在解决共识问题的众所周知的低增益控制器设计方法和稳定线性工厂的输出调节的低增益方法中出现的反馈结构之间的相似性，我们提出了一种新颖的方法解决共识问题的控制器设计技术。我们的技术是基于频域的，与文献中大多数基于状态空间的技术不同。$p^{\mathrm{日}}$所需相位的阶传递函数 $p$在给定的频率下，我们设计的控制器的阶数明显低于共识文献中提出的控制器的阶数。这项工作中开发的技术可以同等地应用于设计降阶控制器，以解决网络中存在已知，统一且任意大的通信和输入延迟的情况下解决上述共识问题。