Consensus of Discrete-Time Linear Multi-Agent Systems with Observer-Type Protocols
Beijing Institute of Technology（北京理工大学）；Peking University（北京大学）；City University of Hong Kong（香港城市大学）
Zhongkui Li, Zhisheng Duan, Guanrong Chen
备注：
18 pages, 6 figures; This paper is an enlarged version of the paper, with the same title, to appear in Discrete and Continuous Dynamical Systems-Series B
发表信息：
Discrete and Continuous Dynamical Systems-Series B 16 (2011) 489-505
This paper concerns the consensus of discrete-time multi-agent systems with linear or linearized dynamics. An observer-type protocol based on the relative outputs of neighboring agents is proposed. The consensus of such a multi-agent system with a directed communication topology can be cast into the stability of a set of matrices with the same low dimension as that of a single agent. The notion of discrete-time consensus region is then introduced and analyzed. For neurally stable agents, it is shown that there exists an observer-type protocol having a bounded consensus region in the form of an open unit disk, provided that each agent is stabilizable and detectable. An algorithm is further presented to construct a protocol to achieve consensus with respect to all the communication topologies containing a spanning tree. Moreover, for the case where the agents have no poles outside the unit circle,an algorithm is proposed to construct a protocol having an origin-centered disk of radius $δ$ ($0<δ<1$) as its consensus region, where $δ$ has to further satisfy a constraint related to the unstable eigenvalues of a single agent for the case where each agent has a least one eigenvalue outside the unit circle. Finally, the consensus algorithms are applied to solve formation control problems of multi-agent systems.
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Beijing Institute of Control Engineering（北京控制工程研究所）；Science and Technology on Space Intelligent Control Laboratory, Beijing Institute of Control Engineering（空间智能控制重点实验室，北京控制工程研究所）
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Technische Universität Berlin（柏林工业大学）；Fraunhofer Heinrich Hertz Institute（弗劳恩霍夫海因里希赫兹研究所）；Max-Planck-Institut für Dynamik komplexer technischer Systeme（复杂技术系统动力学马普研究所）
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