# American Institute of Mathematical Sciences

September  2011, 16(2): 489-505. doi: 10.3934/dcdsb.2011.16.489

## Consensus of discrete-time linear multi-agent systems with observer-type protocols

 1 School of Automation, Beijing Institute of Technology, Beijing 100081, P. R., China 2 State Key Lab for Turbulence and Complex Systems, Department of Mechanics and Aerospace Engineering, College of Engineering, Peking University, Beijing 100871, P. R., China 3 Department of Electronic Engineering, City University of Hong Kong, Hong Kong

Received  December 2009 Revised  October 2010 Published  June 2011

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. Finally, the consensus algorithms are applied to solve formation control problems of multi-agent systems.
Citation: Zhongkui Li, Zhisheng Duan, Guanrong Chen. Consensus of discrete-time linear multi-agent systems with observer-type protocols. Discrete & Continuous Dynamical Systems - B, 2011, 16 (2) : 489-505. doi: 10.3934/dcdsb.2011.16.489
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