@article{f67398bf2a474e7a83503dbbebb66bc9, title = "Consensus of discrete-time linear multi-agent systems with observer-type protocols", abstract = "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. Finally, the consensus algorithms are applied to solve formation control problems of multi-agent systems.", keywords = "Consensus, Consensus region, Discrete-time linear system, Formation control, Multi-agent system, Observer- type protocol", author = "Zhongkui Li and Zhisheng Duan and Guanrong Chen", year = "2011", month = sep, doi = "10.3934/dcdsb.2011.16.489", language = "English", volume = "16", pages = "489--505", journal = "Discrete and Continuous Dynamical Systems - Series B", issn = "1531-3492", publisher = "American Institute of Mathematical Sciences (A I M S Press)", number = "2", }