Computer Science – Systems and Control
Scientific paper
2011-02-28
Discrete and Continuous Dynamical Systems-Series B 16 (2011) 489-505
Computer Science
Systems and Control
18 pages, 6 figures; This paper is an enlarged version of the paper, with the same title, to appear in Discrete and Continuous
Scientific paper
10.3934/dcdsb.2011.16.489
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 $\delta$ ($0<\delta<1$) as its consensus region, where $\delta$ 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.
Chen Guanrong
Duan Zhisheng
Li Zhongkui
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